mitchell_03

mitchell_03, a FreeFem++ code which sets up and solves Mitchell's test problem #3, "linear elasticity", two coupled equations with a mixed derivative in the coupling term, defined on the [-1,+1]x[-1,+1] square, with a slit from (0,0) to (1,0), using parameter values nu = 0.3, E = 1, lambda, and Q.

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: 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_03a defines the "linear elasticity" problem, a coupled system of two equations with a mixed derivative in the coupling term, defined on the [-1,+1]x[-1,+1] square, with a slit from (0,0) to (1,0), using parameter values nu = 0.3, E = 1, lambda = 0.5444837367825, Q = 0.5430755788367.

• mitchell_03a.edp, the input file.
• mitchell_03a.sh, runs FreeFem++ on the input file.
• mitchell_03a.txt, the output file.

• mitchell_03a_mesh.png, a PNG image of the mesh.
• mitchell_03a_u.png, a PNG image of a vector plot of the solution.

mitchell_03b defines the "linear elasticity" problem, a coupled system of two equations with a mixed derivative in the coupling term, defined on the [-1,+1]x[-1,+1] square, with a slit from (0,0) to (1,0), using parameter values nu = 0.3, E = 1, lambda = 0.9085291898461, Q = -0.2189232362488.

• mitchell_03b.edp, the input file.
• mitchell_03b.sh, runs FreeFem++ on the input file.
• mitchell_03b.txt, the output file.

• mitchell_03b_mesh.png, a PNG image of the mesh.
• mitchell_03b_u.png, a PNG image of a vector plot of the solution.