dune-fem-dg 2.11.dev20250115

The Dune FEM module: Discontinuous Galerkin for evolution equations

DUNE-FEM-DG

DUNE-FEM-DG is the implementation of Discontinuous Galerkin schemes using the DUNE-FEM framework. Stabilized DG schemes for hyperbolic as well as a wide range of different primal formulations for elliptic/parabolic problems are implemented. The operators can be used efficiently both in a explicit/matrix free implementation or used to setup a system matrix for use with the linear solvers available in DUNE-FEM.

License

The DUNE-FEM-DG module is available under the GNU General Public License version 2, or (at your option), any later version.

References

A detailed description of how to use the code can be found in the first paper, the description of the schemes can be found in the second and third papers and an overview on performance of the code is given in the forth paper.

• A. Dedner, R. Klöfkorn. Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method. Commun. Appl. Math. Comput., 2021. https://dx.doi.org/10.1007/s42967-021-00134-5.

• S. Brdar, A. Dedner, and R. Klöfkorn. Compact and stable Discontinuous Galerkin methods for convection-diffusion problems. SIAM J. Sci. Comput., 34(1):263-282, 2012. https://dx.doi.org/10.1137/100817528

• A. Dedner and R. Klöfkorn. A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems. J. Sci. Comput., 47(3):365-388, 2011. https://dx.doi.org/10.1007/s10915-010-9448-0

An overview on performance of the code is given in

• R. Klöfkorn. Efficient Matrix-Free Implementation of Discontinuous Galerkin Methods for Compressible Flow Problems. Proceedings of the ALGORITMY 2012. http://www.iam.fmph.uniba.sk/algoritmy2012/zbornik/2Kloefkornf.pdf

By using the code you agree to cite one or both of the first two papers in any publication using this code.

Eye-candy

The avatar of the project shows the solution of the compressible Euler equations in 3D using the parallel-adaptive DUNE-ALUGrid and the DG discretization implemented in DUNE-FEM-DG.

Installation

Using pip

dune-fem-dg can be installed using the Package Index of Python (pip).

pip install dune-fem-dg

See https://dune-project.org/doc/installation-pip/ for a more detailed description.

From source

dune-fem-dg also provides a shell script to install the sources using a specific git branch. Further detailed explanation on the DUNE installation process please read the installation notes https://www.dune-project.org/doc/installation/.

Documentation

A documentation of the Python bindings of DUNE-FEM-DG can be found in

• A. Dedner, R. Klöfkorn. Extendible and Efficient Python Framework for Solving Evolution Equations with Stabilized Discontinuous Galerkin Method. Commun. Appl. Math. Comput., 2021. https://dx.doi.org/10.1007/s42967-021-00134-5.

A documentation for C++ code (and 2.4 release) can be found in

• A. Dedner, S. Girke, R. Klöfkorn, T. Malkmus. The DUNE-FEM-DG module. Archive of Numerical Software 5(1): 21--61. 2017. https://dx.doi.org/10.11588/ans.2017.1.28602

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