FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting

TL;DR

This paper introduces FESTUNG, an open-source MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, focusing on advection operators and slope limiting schemes for 2D time-dependent linear advection equations.

Contribution

It provides a comprehensive, vectorized implementation of DG methods with slope limiting, supporting both MATLAB and GNU Octave, and emphasizes clear code structure and flexibility.

Findings

Implemented general order slope limiting schemes for DG methods.

Supported space/time-varying coefficients in 2D advection.

Ensured full GNU Octave compatibility.

Abstract

This is the second in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source Matlab / GNU Octave toolbox. The intention of this ongoing project is to offer a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix / vector operations and is comprehensively documented. Particular attention was paid to maintaining a direct mapping between discretization terms and code routines as well as to supporting the full code functionality in GNU Octave. The present work focuses on a two-dimensional time-dependent linear advection equation with space / time-varying coefficients, and provides a general order implementation of several slope limiting schemes for the DG method.