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all_the_stones.tex
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\documentclass[a4paper,11pt]{report}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{pdflscape}
\usepackage[cm]{fullpage}
\usepackage{upgreek}
\usepackage{bm}
\usepackage{mdframed}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage[dvipsnames]{xcolor}
\usepackage{dsfont}
\usepackage{gensymb} %\degree
\usepackage{listings}
\usepackage{stmaryrd}
\usepackage{multicol}
\usepackage{lipsum}
\usepackage{verbatim}
\usepackage[colorinlistoftodos,prependcaption,textsize=tiny]{todonotes}
\usepackage{csquotes}
\usepackage{siunitx}
\DeclareSIUnit\year{yr}
\DeclareSIUnit\day{day}
\renewcommand{\chaptername}{Stone}
\input{newcommands}
\usepackage{tikz}
\usetikzlibrary{arrows, arrows.meta}
\usepackage{hyperref}
\hypersetup{
colorlinks,
citecolor=black,
filecolor=black,
linkcolor=violet,
urlcolor=black}
\lstset{
language=Python,
backgroundcolor=\color{white}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}; should come as last argument
basicstyle=\footnotesize, % the size of the fonts that are used for the code
breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace
breaklines=true, % sets automatic line breaking
captionpos=b, % sets the caption-position to bottom
frame=single, % adds a frame around the code
keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible)
keywordstyle=\color{blue}, % keyword style
}
\newcommand{\inpython}{\fbox{\textbf{\large \color{teal} P}}}
\newcommand{\injulia}{\fbox{\textbf{\large \color{purple} J}}}
\newcommand{\infortran}{\fbox{\textbf{\large \color{orange} F}}}
\usepackage{xr}
\externaldocument[MMM-]{manual}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsthm}
\newtheorem*{remark}{Remark}
\newtheorem{problem}{problem:}
\newtheorem{problem-bonus}{problem*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Bibliography stuff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[maxnames=6]{biblatex}
\addbibresource{biblio_geosciences.bib}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\author{C. Thieulot}
\title{All the stones}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{multind}
\makeindex{contributors}
\makeindex{stopics}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\thispagestyle{empty}
\includegraphics[width=0.9\linewidth]{images/frontpage/frontpage.png}
\maketitle
\tableofcontents
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter*{Naming convention for every stone and elefant }
These have evolved in the first two years so that the early stones may not
follow these conventions (yet).
\begin{tabular}{p{2.5cm}p{14cm}}
\hline
Variable & meaning \\
\hline
\hline
{\tt mV} & number $m_\upnu$ of velocity nodes in the element \\
{\tt mP} & number $m_p$ of pressure nodes in the element \\
{\tt mT} & number $m_T$ of temperature nodes in the element \\
{\tt ndofV} & number of velocity degrees of freedom per velocity node \\
{\tt ndofP} & number of pressure degrees of freedom per pressure node \\
{\tt NV} & total number of velocity nodes \\
{\tt NfemV} & total number of velocity degrees of freedom \\
{\tt NfemP} & total number of pressure degrees of freedom \\
{\tt Nfem} & total number of degrees of freedom \\
{\tt nelx,nely,nelz} & number of elements in each direction \\
{\tt nel} & total number of elements \\
{\tt nqel} & number of quadrature points per element \\
{\tt xq,yq,zq} & coordinates of a quadrature point \\
{\tt uq,vq,wq} & velocity at a quadrature point \\
{\tt pq} & pressure at a quadrature point \\
{\tt etaq} & viscosity value at a quadrature point \\
{\tt rhoq} & density value at a quadrature point \\
{\tt dt} & time step $\delta t$\\
{\tt gx,gy,gz} & components of the gravity vector \\
{\tt jcob} & determinant of the Jacobian matrix \\
\hline
\end{tabular}
\vspace{.5cm}
\begin{tabular}{p{3.5cm}p{12.5cm}}
\hline
Array & meaning \\
\hline
\hline
{\tt iconV} & connectivity array for velocity nodes \\
{\tt iconP} & connectivity array for pressure nodes \\
{\tt qcoords\_r} & contains the $r$ coordinates of the {\tt nel} quadrature points \\
{\tt qcoords\_s} & contains the $s$ coordinates of the {\tt nel} quadrature points \\
{\tt qcoords\_t} & contains the $t$ coordinates of the {\tt nel} quadrature points \\
{\tt qweights} & contains the weights associated to the {\tt nel} quadrature points \\
{\tt xV,yV,zV} & coordinates of the {\tt NV} velocity nodes \\
{\tt xP,yP,zP} & coordinates of the {\tt NP} pressure nodes \\
{\tt bc\_fix} & boolean array of size {\tt NfemV}. Is true if a boundary condition
is specify at a dof \\
{\tt bc\_val} & value of the boundary condition at a given dof \\
{\tt u,v,w} & velocity components \\
{\tt p} & pressure \\
{\tt q} & pressure projected onto the velocity nodes\\
{\tt NNNV} & velocity basis functions values at a quadrature point \\
{\tt dNNNVdr} & velocity basis functions derivatives values at a quadrature point \\
{\tt dNNNVds} & velocity basis functions derivatives values at a quadrature point \\
{\tt dNNNVdt} & velocity basis functions derivatives values at a quadrature point \\
{\tt NNNP} & pressure basis functions values at a quadrature point \\
{\tt b\_mat} & elemental gradient matrix ${\bm B}$ \\
{\tt K\_el} & elemental stiffness matrix $\K_{el}$ \\
{\tt G\_el} & elemental gradient matrix $\G_{el}$ \\
{\tt N\_mat} & elemental ${\bm N}$ matrix \\
{\tt a\_mat} & fully assembled Stokes matrix \\
{\tt A\_sparse} & Stokes matrix in {\tt lil\_matrix} format \\
{\tt exx,eyy,exy,...} & components of the strain rate tensor (elemental or nodal array)\\
{\tt tauxx,tauyy,tauxy,...} & components of the deviatoric stress tensor (elemental or nodal array)\\
{\tt jcb} & 2x2 or 3x3 Jacobian matrix \\
{\tt jcbi} & inverse of the Jacobian matrix \\
{\tt rhs} & right hand side vector \\
{\tt sol} & solution vector returned by the solver\\
\hline
\end{tabular}
\vspace{.5cm}
\begin{tabular}{p{2cm}p{14cm}}
\hline
Function & meaning \\
\hline
{\tt NNV} & function which returns the value of all velocity basis functions
${\cal N}_i^\upnu$ at a given location\\
{\tt dNNVdr} & function which returns the value of all velocity basis functions
${\cal N}_i^\upnu$ derivative with respect to $r$ at a given location\\
{\tt dNNVds} & function which returns the value of all velocity basis functions
${\cal N}_i^\upnu$ derivative with respect to $s$ at a given location\\
{\tt dNNVdt} & function which returns the value of all velocity basis functions
${\cal N}_i^\upnu$ derivative with respect to $t$ at a given location\\
{\tt NNP} & function which returns the value of all pressure basis functions
${\cal N}_i^P$ at a given location\\
{\tt bx} & \\
{\tt by} & \\
{\tt bz} & \\
\hline
\end{tabular}
\chapter*{Stone 00: mesh generation in 1D, 2D, 3D \label{f00}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 00
\input{python_codes/fieldstone_00/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Manufactured solution ($Q_1\times P_0$+penalty)\label{f01}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 01
\input{python_codes/fieldstone_01/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Stokes sphere in 2D ($Q_1\times P_0$+penalty) \label{f02}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 02
\input{python_codes/fieldstone_02/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Convection in a 2D box ($Q_1\times P_0$+penalty)\label{f03}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 03
\input{python_codes/fieldstone_03/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The lid driven cavity ($Q_1\times P_0$+penalty) \label{f04}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 04
\input{python_codes/fieldstone_04/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{SolCx benchmark ($Q_1\times P_0$+penalty)\label{f05}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 05
\input{python_codes/fieldstone_05/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{SolKz benchmark ($Q_1\times P_0$+penalty)\label{f06}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 06
\input{python_codes/fieldstone_06/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{SolVi benchmark ($Q_1\times P_0$+penalty) \label{f07}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 07
\input{python_codes/fieldstone_07/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The indentor benchmark ($Q_1\times P_0$+penalty)\label{f08}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 08
\input{python_codes/fieldstone_08/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The annulus benchmark ($Q_1\times P_0$+penalty) \label{f09}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 09
\input{python_codes/fieldstone_09/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Stokes sphere in 3D ($Q_1 \times P_0$+penalty, $Q_2 \times P_0$+penalty)\label{f10}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 10
\input{python_codes/fieldstone_10/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Stokes sphere in 3D ($Q_1\times P_0$ - mixed) \label{f11}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 11
\input{python_codes/fieldstone_11/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{consistent pressure recovery ($Q_1\times P_0$+penalty)\label{f12}} %%%%%%%%%%%%%%%%%%%%%%% 12
\input{python_codes/fieldstone_12/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{the Particle in Cell technique (1) - the effect of averaging ($Q_1\times P_0$+penalty)\label{f13}} %13
\input{python_codes/fieldstone_13/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{solving the full saddle point problem ($Q_1\times P_0$) \label{f14}} %%%%%%%%%%%%%%%%%%%%% 14
\input{python_codes/fieldstone_14/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{saddle point problem with Schur complement approach - benchmark ($Q_1\times P_0$)\label{f15}} % 15
\input{python_codes/fieldstone_15/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{saddle point problem with Schur complement approach - Stokes sphere ($Q_1\times P_0$) \label{f16}} % 16
\input{python_codes/fieldstone_16/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Solving the full saddle point problem in 3D ($Q_1\times P_0$, $Q_2\times Q_1$)\label{f17}} % 17
\input{python_codes/fieldstone_17/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{D\&H mms and more: Solving the full saddle point problem ($Q_2\times Q_1$) \label{f18}} %% 18
\input{python_codes/fieldstone_18/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{D\&H mms: Solving the full saddle point problem ($Q_3\times Q_2$) \label{f19}} %%%%%%%%%% 19
\input{python_codes/fieldstone_19/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The Busse benchmark ($Q_1\times P_0$) \label{f20}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 20
\input{python_codes/fieldstone_20/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The annulus benchmark ($Q_2\times Q_1$) \label{f21}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 21
\input{python_codes/fieldstone_21/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The stabilised $Q_1 \times Q_1$ element \label{f22}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 22
\input{python_codes/fieldstone_22/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{compressible flow (1) - analytical benchmark ($Q_1\times P_0$)\label{f23}} %%%%%%%%%%%%%%% 23
\input{python_codes/fieldstone_23/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{compressible flow (2) - convection box ($Q_1\times P_0$)\label{f24}} %%%%%%%%%%%%%%%%%%%%% 24
\input{python_codes/fieldstone_24/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Rayleigh-Taylor instability (1) - instantaneous ($Q_2\times Q_1$, $Q_2\times P_{-1}$)\label{f25}} % 25
\input{python_codes/fieldstone_25/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Slab detachment benchmark (1) - instantaneous ($Q_1\times P_0$)\label{f26}} %%%%%%%%%%%%%% 26
\input{python_codes/fieldstone_26/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Consistent Boundary Flux ($Q_1\times P_0$)\label{f27}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 27
\input{python_codes/fieldstone_27/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{convection 2D box - Tosi \etal, 2015 ($Q_1\times P_0$) \label{f28}} %%%%%%%%%%%%%%%%%%%%%% 28
\input{python_codes/fieldstone_28/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{open boundary conditions ($Q_1\times P_0$)\label{f29}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 29
\input{python_codes/fieldstone_29/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{conservative velocity interpolation \label{f30}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 30
\input{python_codes/fieldstone_30/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{conservative velocity interpolation 3D \label{f31}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 31
\input{python_codes/fieldstone_31/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{2D analytical sol. from stream function ($Q_1\times P_0$)\label{f32}} %%%%%%%%%%%%%%%%%%%% 32
\input{python_codes/fieldstone_32/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Convection in an annulus ($Q_1\times P_0$) \label{f33}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 33
\input{python_codes/fieldstone_33/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{2D plane strain elastic problems ($Q_1$)\label{f34}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 34
\input{python_codes/fieldstone_34/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{analytical sol. in annulus from stream function ($Q_1\times P_0$) \label{f35}} %%%%%%%%%%% 35
\input{python_codes/fieldstone_35/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{the annulus geometry elastic aquarium ($Q_1$)\label{f36}}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 36
\input{python_codes/fieldstone_36/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{marker advection and population control \label{f37}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 37
\input{python_codes/fieldstone_37/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{convection in a 700km box with T b.c. at the top ($Q_1\times P_0$-penalty) \label{f38}} % 38
\input{python_codes/fieldstone_38/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The dilation rate approach of \textcite{chpe15} (\QtwoQone) \label{f39}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 39
\input{python_codes/fieldstone_39/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Instantaneous Rayleigh-Taylor instability (\QtwoQone) \label{f40}} %%%%%%%%%%%%%%%%%%%%%%% 40
\input{python_codes/fieldstone_40/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Stokes flow and structural restoration (\QtwoQone) \label{f41}} %%%%%%%%%%%%%%%%%%%%%%%%%% 41
\input{python_codes/fieldstone_41/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The no flow test (\QonePzero, \QtwoQone, \QthreeQtwo, \QfourQthree)\label{f42}} %%%%%%%%%% 42
\input{python_codes/fieldstone_42/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Time-dependent advection problems ($Q_1$, $Q_2$)\label{f43}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%% 43
\input{python_codes/fieldstone_43/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{the flat slab \label{f44}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 44
\input{python_codes/fieldstone_44/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Rotating cone on a triangular ($P_1$) mesh\label{f45}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 45
\input{python_codes/fieldstone_45/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{MMS1 with Crouzeix-Raviart ($P_2^+\times P_{-1}$) elements \label{f46}} %%%%%%%%%%%%%%%%% 46
\input{python_codes/fieldstone_46/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{triangular MINI ($P_1^+\times P_1$) element \label{f47}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 47
\input{python_codes/fieldstone_47/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{D\&H with \QonePzero, \QtwoQone, \QthreeQtwo and \QfourQthree elements \label{f48}} %%%%%% 48
\input{python_codes/fieldstone_48/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Consistent Boundary Flux method on D\&H benchmark with 4 elements \label{f49}} %%%%%%%%%%% 49
\input{python_codes/fieldstone_49/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Lithosphere extension (\QtwoQone)\label{f50}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 50
\input{python_codes/fieldstone_50/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Convection in a triangular domain (MINI)\label{f51}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 51
\input{python_codes/fieldstone_51/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Serendipity element in 2D ($Q_2\times Q_1$, $Q_2^{(8)}\times Q_1$, $QH8-C1\times Q_1$) \label{f52}} % 52
\input{python_codes/fieldstone_52/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The sinking block benchmark ($Q_2\times Q_1$, $Q_2^{(8)}\times Q_1$) \label{f53}} %%%%%%%%%%%%%%%%%%% 53
\input{python_codes/fieldstone_53/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Arbitrary Lagrangian Eulerian formulations \label{f54}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 54
\input{python_codes/fieldstone_54/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Subduction as a thin-sheet problem \label{f55}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 55
\input{python_codes/fieldstone_55/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The Diamond-square algorithm \label{f56}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 56
\input{python_codes/fieldstone_56/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{DG-FEM: 1D steady state diffusion \label{f57}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 57
\input{python_codes/fieldstone_57/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Elastic disk under compression \label{f58}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 58
\input{python_codes/fieldstone_58/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Ice Flow Down an Inclined Plane \label{f59}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 59
\input{python_codes/fieldstone_59/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{DG-FEM: 1D advection \label{f60}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 60
\input{python_codes/fieldstone_60/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Channel flow with Herschel-Bulkley rheology (\QtwoQone) \label{f61}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 61
\input{python_codes/fieldstone_61/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Subduction a la Quinquis Case 1 ($P_2^+\times P_{-1}$) \label{f62}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 62
\input{python_codes/fieldstone_62/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{failure in cemented granular material \label{f63}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 63
\input{python_codes/fieldstone_63/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Elasto-viscous benchmarks \label{f64}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 64
\input{python_codes/fieldstone_64/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{steady-state advection-diffusion ($Q_1$) \label{f65}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 65
\input{python_codes/fieldstone_65/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{something about sph \label{f66}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 66
\input{python_codes/fieldstone_66/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Newtonian subduction setups (sinking block, subduction)\label{f67}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 67
\input{python_codes/fieldstone_67/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{the corner flow - Subduction benchmark (2) \label{f68}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 68
\input{python_codes/fieldstone_68/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Spherical shell \label{f69}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 69
\input{python_codes/fieldstone_69/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Visco-Viscoplastic rheology in crustal model ($Q_2\times Q_1$)\label{f70}} %%%%%%%%%%%%%%%%%%%%%%%%%% 70
\input{python_codes/fieldstone_70/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{S40RTS in an annulus \label{f71}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 71
\input{python_codes/fieldstone_71/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{quadrilateral MINI - the $Q_1^+\times Q_1$ element \label{f72}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 72
\input{python_codes/fieldstone_72/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{using python functionalities (\QonePzero + penalty)\label{f73}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 73
\input{python_codes/fieldstone_73/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{the annulus benchmark with $Q_1^+\times Q_1$ elements (MINI) \label{f74}} %%%%%%%%%%%%%%%%%%%%%%%%%%% 74
\input{python_codes/fieldstone_74/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{the 3D stokes sphere with $Q_1^{+}\times Q_1$ elements (MINI) \label{f75}} %%%%%%%%%%%%%%%%%%%%%%%%%%%% 75
\input{python_codes/fieldstone_75/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{mms and stokes sphere with $Q_2\times P_{-1}$ elements \label{f76}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 76
\input{python_codes/fieldstone_76/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Rotated $Q_1\times P_0$ element \& DSSY element \label{f77}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 77
\input{python_codes/fieldstone_77/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{$Q_1\times P_0$ macro-element \label{f78}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 78
\input{python_codes/fieldstone_78/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{DG-FEM: 2D steady state diffusion \label{f79}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 79
\input{python_codes/fieldstone_79/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Fortin's $Q_1^+\times P_0$ in 2D \label{f80}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 80
\input{python_codes/fieldstone_80/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Fortin's $Q_1^+\times P_0$ in 3D \label{f81}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 81
\input{python_codes/fieldstone_81/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The 3D MINI element with 2 bubble functions ($Q_1^{++}\times Q_1$) \label{f82}} %%%%%%%%%%%%%%%%%%%%% 82
\input{python_codes/fieldstone_82/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Thermal structure of oceanic and continental lithosphere ($Q_1,Q_2$)\label{f83}} %%%%%%%%%%%%%%%%%%%% 83
\input{python_codes/fieldstone_83/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{computing gravity above objects \label{f84}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 84
\input{python_codes/fieldstone_84/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Using the S20RTS and S40RTS datasets \label{f85}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 85
\input{python_codes/fieldstone_85/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Thermal re-equilibrium of the Lith. Mantle during post-rift stage ($Q_1\times P_0$)\label{f86}} %%%% 86
\input{python_codes/fieldstone_86/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Newton method for power-law rheologies ($Q_2\times Q_1$) \label{f87}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 87
\input{python_codes/fieldstone_87/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{convection in a stratified mantle ($Q_1 \times P_0$, $Q_2\times Q_1$, $Q_3\times Q_2$) \label{f88}} %%%%%%%%%%%% 88
\input{python_codes/fieldstone_88/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{on the topic of integrated deformation \label{f89}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 89
\input{python_codes/fieldstone_89/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Thick-walled elastic cylinder under uniform boundary pressure (axisymmetric) \label{f90}} %%%%%%%%%%%%%%%%%%%%%%%%% 90
\input{python_codes/fieldstone_90/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Stokes sphere in a cylinder, axisymmetric formulation ($Q_2\times Q_1$) \label{f91}} %%%%%%%%%%%%%%% 91
\input{python_codes/fieldstone_91/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Stokes sphere in a cylinder, axisymmetric formulation, $P_2^+\times P_{-1}$ \label{f92}} %%%%%%%%%%% 92
\input{python_codes/fieldstone_92/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Buoyancy-driven flow with ($P_2^+\times P_{-1}$) \label{f93}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 93
\input{python_codes/fieldstone_93/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{visualising UUP07 in Paraview \label{f94}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 94
\input{python_codes/fieldstone_94/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{van Keken \etal R-T instability with mesh adaptivity ($P_2^+\times P_{-1}$) \label{f95}} %%%%%%%%%%% 95
\input{python_codes/fieldstone_95/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Blob in axisymmetric planet ($P_2\times P_1$, $P_2^+\times P_{-1}$) \label{f96}} %%%%%%%%%%%%%%%%%%% 96
\input{python_codes/fieldstone_96/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{using the CRUST 1.0 dataset \label{f97}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 97
\input{python_codes/fieldstone_97/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Single WINTERC layer gravity benchmark \label{f98}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 98
\input{python_codes/fieldstone_98/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{reading in the whole WINTERC 5.4 dataset \label{f99}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 99
\input{python_codes/fieldstone_99/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{the MOLA Mars topography \& computing gravity \label{f100}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 100
\input{python_codes/fieldstone_100/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Y12M solver for $Q_1\times P_0$+penalty Fortran codes \label{f101}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 101
\input{python_codes/fieldstone_101/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{conformal mesh refinement in 2D \label{f102}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 102
\input{python_codes/fieldstone_102/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{conformal mesh refinement in 3D \label{f103}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 103
\input{python_codes/fieldstone_103/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{grad-div stabilisation ($Q_2\times Q_1$, $Q_2 \times P_{-1}$) \label{f104}} %%%%%%%%%%%%%%%%%%%%%%%% 104
\input{python_codes/fieldstone_104/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{solving the flexure equation with FDM \label{f105}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 105
\input{python_codes/fieldstone_105/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{plumes in axisymmetric chunk ($Q_2\times Q_1$) \label{f106}} %%%%%%%%%%%%%%%%%%%%%%%%%%%% 106
\input{python_codes/fieldstone_106/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Convection in a porous medium \label{f107}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 107
\input{python_codes/fieldstone_107/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{topography above lower crustal bordering the Tibetan plateau \label{f108}} %%%%%%%%%%%%%%% 108
\input{python_codes/fieldstone_108/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Poiseuille flow with obstacle in 3D ($Q_2\times Q_1$) \label{f109}} %%%%%%%%%%%%%%%%%%%%%% 109
\input{python_codes/fieldstone_109/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Convection in a 2D box - BA vs EBA ($Q_2\times Q_1$) \label{f110}} %%%%%%%%%%%%%%%%%%%%%%% 110
\input{python_codes/fieldstone_110/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Manufactured solution for compressible elastic deformation in a disc\label{f111}} %%%%%%%% 111
\input{python_codes/fieldstone_111/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{MINI, $P_2\times P_1$, $Q_2\times Q_1$, $Q_2\times P_{-1}$ and C-R elts\label{f112}} %%%% 112
\input{python_codes/fieldstone_112/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Gravity of a const. $\rho$ tetrahedron following Werner \& Scheeres (1997) \label{f113}} % 113
\input{python_codes/fieldstone_113/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Joint Gravity and Stokes inversion of a 2D circular anomaly \label{f114}} %%%%%%%%%%%%%%%% 114
\input{python_codes/fieldstone_114/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{$Q_1\times P_0$-stab element for isoviscous flow \label{f115}} %%%%%%%%%%%%%%%%%%%%%%%%%%% 115
\input{python_codes/fieldstone_115/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{$Q_1\times P_0$-stab element with viscosity contrasts\label{f116}} %%%%%%%%%%%%%%%%%%%%%%% 116
\input{python_codes/fieldstone_116/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{circular inclusion with bespoke mesh \label{f117}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 117
\input{python_codes/fieldstone_117/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{subduction initiation in the 80's ($Q_2\times Q_1$) \label{f118}} %%%%%%%%%%%%%%%%%%%%%%%% 118
\input{python_codes/fieldstone_118/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{on computing the lithostatic pressure in geodynamical models \label{f119}} %%%%%%%%%%%%%%% 119
\input{python_codes/fieldstone_119/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{2D Stokes flow. Which FE pair is best? \label{f120}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 120
\input{python_codes/fieldstone_120/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Olivine deformation maps (Gueydan \& Pr{\'e}cigout, 2014) \label{f121}} %%%%%%%%%%%%%%%%% 121
\input{python_codes/fieldstone_121/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Runge-Kutta methods \& particle advection \label{f122}}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 122
\input{python_codes/fieldstone_122/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Boussinesq \& Love elastic problems\label{f123}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 123
\input{python_codes/fieldstone_123/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Plate with a hole elastic problems \label{f124}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 124
\input{python_codes/fieldstone_124/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Building Voronoi cells \label{f125}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 125
\input{python_codes/fieldstone_125/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Darcy stuff\label{f126}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 126
\input{python_codes/fieldstone_126/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{circular inclusion in simple shear ($P_2^+\times P_{-1}$)\label{f127}} %%%%%%%%%%%%%%%%%%% 127
\input{python_codes/fieldstone_127/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{fluid flow in porous media - Simpson book chapter 10 ($Q_1$)\label{f128}} %%%%%%%%%%%%%%%% 128
\input{python_codes/fieldstone_128/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Visco-elastic materials - Simpson book chapter 12 ($Q_2$)\label{f129}} %%%%%%%%%%%%%%%%%%% 129
\input{python_codes/fieldstone_129/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Reaction-diffusion ($Q_1$) - Simpson book chapter 7\label{f130}} %%%%%%%%%%%%%%%%%%%%%%%%% 130
\input{python_codes/fieldstone_130/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{creating triangular meshes with python \label{f131}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 131
\input{python_codes/fieldstone_131/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{gravity field of a mass circle\label{f132}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 132
\input{python_codes/fieldstone_132/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The annulus benchmark ($Q_2\times Q_1$) with Doube Jacobian \label{133}} %%%%%%%%%%%%%%%%% 133
\input{python_codes/fieldstone_133/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{CMT Catalog Files\label{f134}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 134
\input{python_codes/fieldstone_134/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{SLAB2 data visualisation\label{f135}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 135
\input{python_codes/fieldstone_135/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{RUM slabs visualisation\label{f136}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 136
\input{python_codes/fieldstone_136/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Configurational entropy \label{f137}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 137
\input{python_codes/fieldstone_137/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Magnetic Terrain Effect \label{f138}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 138
\input{python_codes/fieldstone_138/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Evolution of a 1D River Profile\label{f139}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 139
\input{python_codes/fieldstone_139/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Evolution of a Fluvially Dissected Landscape \label{f140}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 140
\input{python_codes/fieldstone_140/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{The 'Beaumont' mantle temperature trick \label{f141}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 141
\input{python_codes/fieldstone_141/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Calculating stress and strain rate in 2D viscous inclusion-matrix systems \label{f142}} %%%%%%%%%%%% 142
\input{python_codes/fieldstone_142/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Passive margins getting squeezed in the mantle convection vice \label{f143}} %%%%%%%%%%%%%%%%%%%%%%% 143
\input{python_codes/fieldstone_143/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Dave's magma \label{f144}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 144
\input{python_codes/fieldstone_144/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Converting vtu files to png or ascii \label{f145}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 145
\input{python_codes/fieldstone_145/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Jan's project \label{f146}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 146
\input{python_codes/fieldstone_146/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Solving the Stokes system with LINALG and more} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 147
\input{python_codes/fieldstone_147/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Erik's project \label{f148}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 148
\input{python_codes/fieldstone_148/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{van Keken et al 2008 benchmark with bespoke quad mesh\label{f149}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 149
\input{python_codes/fieldstone_149/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Optimisation of FE matrix building process \label{f150}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 150
\input{python_codes/fieldstone_150/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Free slip on curved geometries (\QtwoQone)\label{f151}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 151
\input{python_codes/fieldstone_151/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Temperature in mantle wedge (van Keken et al 2008) \label{f152}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 152
\input{python_codes/fieldstone_152/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Vorticity-Streamfunction - isoviscous 2D case with free slip\label{f153}} %%%%%%%%%%%%%%%%%%%%%%%%%% 153
\input{python_codes/fieldstone_153/text}
\chapter{Vorticity-Streamfunction - isoviscous 2D case with no slip\label{f154}} %%%%%%%%%%%%%%%%%%%%%%%%%%%% 154
\input{python_codes/fieldstone_154/text}
\chapter{Vorticity-Streamfunction - Convection in 2D box \label{f155}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 155
\input{python_codes/fieldstone_155/text}
\chapter{Vorticity-Streamfunction \& the Lorenz equations - Kellogg \& Turcotte (1990) \label{f156}} %%%%%%% 156
\input{python_codes/fieldstone_156/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Solving the 1D diffusion equation with the Method of Lines \label{f157}} %%%%%%%%%%%%%%%%%%%%%%%%%% 157
\input{python_codes/fieldstone_157/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Solving the diagenetic A-D-R equations with the Method of Lines \label{f158}} %%%%%%%%%%%%%%%%%%%%%% 158
%\input{python_codes/fieldstone_158/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Computing plastic yield envelopes \label{f159}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 159
\input{python_codes/fieldstone_159/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{A simple look at dynamic topography \label{f160}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 160
\input{python_codes/fieldstone_160/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Implementing the $Q_{2,1}\times Q_{1,2} \times Q_{1}'$ element \label{f161}} %%%%%%%%%%%%%%%%%% 161
\input{python_codes/fieldstone_161/text} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter{Title of the stone}
\input{python_codes/template} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendix
\chapter{Classification}
\section{
Stones I wrote/adapted/used for reviewing a paper}
\section{
Stones which are replicating a paper}
\includegraphics[width=2cm]{images/pictograms/replication}
3, 28, 38, 39, 59, 63, 142, 143
\section{
Stones which served as a basis for a publication}
\section{
Stones (partially) based on BSc/MSc thesis}
\includegraphics[width=2cm]{images/pictograms/bsc}
\includegraphics[width=2cm]{images/pictograms/msc}
96
\printbibliography
\newpage
\printindex{contributors}{Contributors}
\printindex{stopics}{Elements}
\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\addcontentsline{toc}{chapter}{\protect\numberline{} Naming convention}