Element Schur complement preconditioners

This repository contains the code which produces the results for An element-based preconditioner for mixed finite element problems, Tyrone Rees and Michael Wathen, 2020

Code DOI:

Install instructions

The only external dependency is Firedrake, which can be installed following the instructions from https://www.firedrakeproject.org/download.html. Once Firedrake is installed correctly then this will create a new python environment that needs to be activated.

To finish the installation, run pip install . from the root directory. This will install the repository plus the additional pandas requirement.

Running

There are three examples presented here:

• Stokes flow
• Mixed formulation of Maxwell's equations
• Navier-Stokes equations These examples are store in individual folders within the ElementSchur/examples. To find install instructions for each example run python filename.py –help.

Note: For the backwards facing step examples (for Stokes and Navier-Stokes) one will need to make the mesh files which are found in ElementSchur/ElementSchur/mesh. There are Makefile within these folders which will create the appropriate meshes. Firedrake uses the meshing software Gmsh https://gmsh.info/.

The script ElementSchur/examples/run_script was used to create the results presented in the paper.