mitchell_09

mitchell_09, a FreeFem++ code which sets up and solves Mitchell's problem #9, "the wave front".

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:

mitchell_09a defines the "wave front" problem on the [0,+1]x[0,+1] square with parameters ALPHA = 20, XC = -0.05, YC = -0.05, R0 = 0.7.

• mitchell_09a.edp, the input file.
• mitchell_09a.sh, runs FreeFem++ on the input file.
• mitchell_09a.txt, the output file.

• mitchell_09a_mesh.png, a PNG image of the mesh.
• mitchell_09a_u.png, a PNG image of a contour plot of the solution.

mitchell_09b defines the "wave front" problem on the [0,+1]x[0,+1] square with parameters ALPHA = 1000, XC = -0.05, YC = -0.05, R0 = 0.7.

• mitchell_09b.edp, the input file.
• mitchell_09b.sh, runs FreeFem++ on the input file.
• mitchell_09b.txt, the output file.

• mitchell_09b_mesh.png, a PNG image of the mesh.
• mitchell_09b_u.png, a PNG image of a contour plot of the solution.

mitchell_09c defines the "wave front" problem on the [0,+1]x[0,+1] square with parameters ALPHA = 1000, XC = 1.5, YC = 0.25, R0 = 0.92.

• mitchell_09c.edp, the input file.
• mitchell_09c.sh, runs FreeFem++ on the input file.
• mitchell_09c.txt, the output file.

• mitchell_09c_mesh.png, a PNG image of the mesh.
• mitchell_09c_u.png, a PNG image of a contour plot of the solution.

mitchell_09d defines the "wave front" problem on the [0,+1]x[0,+1] square with parameters ALPHA = 50, XC = 0.5, YC = 0.5, R0 = 0.25.

• mitchell_09d.edp, the input file.
• mitchell_09d.sh, runs FreeFem++ on the input file.
• mitchell_09d.txt, the output file.

• mitchell_09d_mesh.png, a PNG image of the mesh.
• mitchell_09d_u.png, a PNG image of a contour plot of the solution.