FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation. (15th June 2018)

• Record Type: Journal Article
• Authors: Jaust, Alexander; Reuter, Balthasar; Aizinger, Vadym; Schütz, Jochen; Knabner, Peter
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 12(2018)
• Page Start: 4505
• Page End: 4533
• Publication Date: 2018-06-15
• Subjects: MATLAB -- GNU Octave -- Hybridized discontinuous Galerkin (HDG) method -- Vectorization -- Open source -- Diagonally implicit Runge–Kutta method (DIRK); Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.03.045
• Languages: English
• ISSNs: 0898-1221

Abstract

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 is 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 a 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.