MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs

TL;DR

MooAFEM is an accessible, object-oriented Matlab code for adaptive finite element methods in 2D, capable of handling nonlinear elliptic PDEs with high flexibility and efficiency.

Contribution

It introduces a fully vectorized, object-oriented Matlab implementation for adaptive FEM with arbitrary polynomial order and general coefficients, suitable for nonlinear PDEs.

Findings

Demonstrates flexibility through various mesh refinement routines.

Shows efficiency with numerical experiments.

Handles nonlinear PDEs via iterative linearization.

Abstract

We present an easily accessible, object oriented code (written exclusively in Matlab) for adaptive finite element simulations in 2D. It features various refinement routines for triangular meshes as well as fully vectorized FEM ansatz spaces of arbitrary polynomial order and allows for problems with very general coefficients. In particular, our code can handle problems typically arising from iterative linearization methods used to solve nonlinear PDEs. Due to the object oriented programming paradigm, the code can be used easily and is readily extensible. We explain the basic principles of our code and give numerical experiments that underline its flexibility as well as its efficiency.