Unified Implementation of Finite Element Methods involving Jumps and Averages in Matlab

TL;DR

This paper presents a unified Matlab implementation framework for finite element methods involving jumps and averages, including adaptive Poisson and interior penalty biharmonic methods, with potential extension to other Galerkin-based techniques.

Contribution

It introduces a comprehensive Matlab implementation approach for various finite element methods involving jumps and averages, facilitating extensions to other Galerkin methods.

Findings

Unified Matlab code for finite element methods involving jumps and averages.

Implementation of adaptive finite element methods for Poisson equation.

Implementation of $C^0$ interior penalty methods for biharmonic equation.

Abstract

We provide unified implementations of the finite element methods involving jumps and averages in Maltab by combing the use of the software package varFEM, including the adaptive finite element methods for the Poisson equation and the $C^0$ interior penalty methods for the biharmonic equation. The design ideas can be extended to other Galerkin-based methods, for example, the discontinuous Galerkin methods and the virtual element methods.