dune-fem-dg 2.9.0.dev20220426

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 the schemes can be found in the first two papers and an overview on performance of the code is given in the third paper.

• 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. http://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. http://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 for the 2.4 release can be found in

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

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