mitchell_10

mitchell_10, a FreeFem++ code which sets up and solves Mitchell's problem 10, "the interior line singularity".

Licensing:

The information on this web page is distributed under the MIT license.

Reference:

A web site at NIST describes these and many other problems: https://math.nist.gov/amr-benchmark/index.html

1. Frederic Hecht,
   New development in FreeFem++,
   Journal of Numerical Mathematics,
   Volume 20, Number 3-4, 2012, pages 251-265.
2. William Mitchell,
   A collection of 2D elliptic problems for testing adaptive grid refinement algorithms,
   Applied Mathematics and Computation,
   Volume 220, 1 September 2013, pages 350-364.
3. Pedro Morin, Ricardo Nochetto, Kunibert Siebert,
   Data oscillation and convergence of adaptive FEM,
   SIAM Journal on Numerical Analysis,
   Volume 38, Number 2, 2000, pages 466-488.

Examples and Tests:

mitchell_10a defines the "interior line singularity" problem on the [-1,+1]x[-1,+1] square with parameters ALPHA = 2.5, BETA = 0.0.

• mitchell_10a.edp, the input file.
• mitchell_10a.sh, runs FreeFem++ on the input file.
• mitchell_10a.txt, the output file.

• mitchell_10a_mesh.png, a PNG image of the mesh.
• mitchell_10a_u.png, a PNG image of a contour plot of the solution.

mitchell_10b defines the "interior line singularity" problem on the [-1,+1]x[-1,+1] square with parameters ALPHA = 1.1, BETA = 0.0.

• mitchell_10b.edp, the input file.
• mitchell_10b.sh, runs FreeFem++ on the input file.
• mitchell_10b.txt, the output file.

• mitchell_10b_mesh.png, a PNG image of the mesh.
• mitchell_10b_u.png, a PNG image of a contour plot of the solution.

mitchell_10c defines the "interior line singularity" problem on the [-1,+1]x[-1,+1] square with parameters ALPHA = 1.5, BETA = 0.6.

• mitchell_10c.edp, the input file.
• mitchell_10c.sh, runs FreeFem++ on the input file.
• mitchell_10c.txt, the output file.

• mitchell_10c_mesh.png, a PNG image of the mesh.
• mitchell_10c_u.png, a PNG image of a contour plot of the solution.