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

摘要

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