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.
%0 Journal Article
%1 jaust2018festung
%A Jaust, Alexander
%A Reuter, Balthasar
%A Aizinger, Vadym
%A Schütz, Jochen
%A Knabner, Peter
%D 2018
%J Computers & Mathematics with Applications
%K 65-04-numerical-analysis-software-source-code 65n30-pdes-bvps-finite-elements hybridized-discontinuous-galerkin
%N 12
%P 4505-4533
%R 10.1016/j.camwa.2018.03.045
%T FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation
%U https://www.sciencedirect.com/science/article/pii/S0898122118301895
%V 75
%X 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.
@article{jaust2018festung,
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.},
added-at = {2021-09-16T02:43:06.000+0200},
author = {Jaust, Alexander and Reuter, Balthasar and Aizinger, Vadym and Schütz, Jochen and Knabner, Peter},
biburl = {https://www.bibsonomy.org/bibtex/259726bb835809f86fddf0120906e4c4e/gdmcbain},
doi = {10.1016/j.camwa.2018.03.045},
interhash = {db791936a7aa072f2a74d0ecd33f1ecd},
intrahash = {59726bb835809f86fddf0120906e4c4e},
issn = {0898-1221},
journal = {Computers & Mathematics with Applications},
keywords = {65-04-numerical-analysis-software-source-code 65n30-pdes-bvps-finite-elements hybridized-discontinuous-galerkin},
number = 12,
pages = {4505-4533},
timestamp = {2021-09-16T02:43:06.000+0200},
title = {FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation},
url = {https://www.sciencedirect.com/science/article/pii/S0898122118301895},
volume = 75,
year = 2018
}