FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation
For researchers and engineers using MATLAB/GNU Octave, this provides an accessible, documented implementation of HDG for rapid prototyping of small to medium-scale applications.
This paper extends the FESTUNG toolbox with a hybridized discontinuous Galerkin (HDG) formulation for linear advection problems, demonstrating that HDG reduces global degrees of freedom compared to standard DG while maintaining accuracy.
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.