The code for interpolation error constants estimation
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mesh
mode_swith_interface
verified_eig_estimation
LICENSE
README.md
constant_c1_1.m
constant_c1_2.m
constant_c1_3.m
constant_c2_3.m
constant_crouzeix_raviart.m
constant_fujino_morley.m
create_matrix_crouzeix_raviart.m
create_matrix_morley.m
est_min_eig.m
get_max_edge_length.m
get_mesh.m
is_edge_on_bd_edge_of_tri_domain.m
is_node_on_edge.m
main.m
my_intlab_mode_config.m
my_ldl.m

README.md

Rigorous interpolation error constant estimation (alpha version)

Xuefeng LIU

First version: 2018/09/26

Running environment

  • The codes run on latest MATLAB environment along with INTLAB toolbox (http://www.ti3.tu-harburg.de/rump/intlab/).
  • Since Octave does not supply ldl function for indefinite symmetric matrix, the rigorous evaluation is not available for Octave.

Configuration

Edit my_intlab_mode_config.m to configure the computing environment.

%The path of the codes for switch between verified computing and approximate computing.
addpath('./mode_swith_interface/');  

%The path of the library of verified eigenvalue estimation for matrix.
addpath('./verified_eig_estimation/'); 

%The path of INTLAB toolbox and initialization.
addpath('~/app/Intlab_V9/');
startintlab;

global INTERVAL_MODE;

%INTERVAL_MODE=1; for rigorous computing based on interval arithmetic.
%INTERVAL_MODE=0; for approximate computing with rounding error inside.
INTERVAL_MODE=1;

Remeber to run "my_intlab_mode_config" before other codes.

How to use it?

For the purpose of rigorous computation, please run the code in MATLAB along with the INTLAB toolbox.

The code has two running mode: approximate evaluation and verified evaluation.

To swith between each other, please set the value of INTERVAL_MODE.

  • INTERVAL_MODE=0: approximate computation mode.
  • INTERVAL_MODE=1: verified computation mode. It takes longer time that approximate computation mode. So be careful with the mesh size, which should not be too small. (To start around h=1/16 is recommended.)

A sample usage can be found in main.m.