MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs
Michael Innerberger, Dirk Praetorius
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.
Topics & Concepts
Finite element methodNonlinear systemComputer scienceMATLABLinearizationAdaptive mesh refinementComputational sciencePolygon meshCode (set theory)Applied mathematicsAlgorithmMathematicsMathematical optimizationProgramming languageComputer graphics (images)ThermodynamicsPhysicsQuantum mechanicsSet (abstract data type)Advanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringElectromagnetic Simulation and Numerical Methods