Benchmark

Description

The aim of this benchmark is to provide a number of test cases in order to compare the properties (convergence, robustness...) of existing discretization schemes for anisotropic diffusion problems using general grids.

The participants should choose their favorite FV scheme, and try to run it on the test cases provided in the file bench.pdf available on this web site.

For each test case, we propose some meshes in the directory Meshes which will be used for the comparison between the various schemes.

The corresponding data files are given in the different formats which are explained in the README file of the web site. An example of mesh with the formats described in the README file is given on the picture test.eps. For any related question to these meshes or formats please get in touch with one of the organizers:

• herbin@cmi.univ-mrs.fr
• fhubert@cmi.univ-mrs.fr

The scheme and the numerical results should be described in an article, the format of which is given in the file template.tex (see also template.pdf)

The scheme which is used should be described in the introduction of the paper, along with the known (mathematically proven) results of convergence, stability, or error estimates.

In order to facilitate the programming, some FORTRAN subroutines giving the source terms, the diffusion tensors, the exact solutions and their derivatives (when available), are given in the file sources.f90 available on this web site.

One may submit a benchmark paper even if only a partial number of test cases and meshes are performed. The submission must be made via the same interface as the one used for the submission of regular papers, using "BENCH_<your last name>" as last name.

Please make sure to register on the web site for the benchmark if you intend to participate, since all updates will be sent to the benchmark mailing list produced by the registrations.

Benchmark session and poster style

The benchmark session will be organized as follows:

• There will be a general benchmark presentation, with a synthesis of the some of the results collected from the benchmark, by R. Herbin and F. Hubert.
• Then there will be a poster session so that each participant can present the detailed results.
• Finally, a discussion session is planned, where each participant may wish to present some other challenging problems where the studied method passes or fails (the idea is to give some perspectives for future research and benchmarks), or new developments of the method.