FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation

TL;DR

FESTUNG is an open-source MATLAB/GNU Octave toolbox that implements hybridized discontinuous Galerkin methods, enabling rapid prototyping for small to medium applications with a focus on linear advection problems.

Contribution

This paper introduces a hybridized DG formulation within FESTUNG, enhancing the toolbox with a new method for linear advection and detailed implementation aligned with standard DG approaches.

Findings

Hybridized DG scheme formulated for linear advection

Performance comparison shows efficiency of hybridized approach

Fully vectorized implementation ensures compatibility and ease of use

Abstract

The third paper in our series on open source MATLAB / GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation. The main aim of this ongoing work is to develop rapid prototyping techniques covering a range of standard DG methodologies and suitable for small to medium sized applications. Our FESTUNG package relies on fully vectorized matrix / vector operations throughout, and all details of the implementation are fully documented. Once again, great care was taken to maintain a direct mapping between discretization terms and code routines as well as to ensure full compatibility to GNU Octave. The current work formulates a hybridized DG scheme for linear advection problem, describes hybrid approximation spaces on the mesh skeleton, and compares the performance of this discretization to the standard (element-based) DG method for different polynomial orders.