mitchell_07

mitchell_07, a FreeFem++ code which sets up and solves Mitchell's problem #7, "boundary line singularity".

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Reference:

A web site at NIST describes these and many other problems: http://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.

Source code:

The "boundary line singularity" problem is defined on the [0,+1]x[0,+1] square. There is a singularity in the right hand side function F(X,Y), at the left boundary. We use the parameter value ALPHA = 0.6.

• mitchell_07.edp, the input file.
• mitchell_07.sh, runs FreeFem++ on the input file.
• mitchell_07.txt, the output file.

• mitchell_07_mesh.png, a PNG image of the mesh.
• mitchell_07_u.png, a PNG image of a contour plot of the solution.