MITCHELL_DEALII
Mitchell Elliptic Test Problems for DEAL.II

MITCHELL_DEALII, example programs which set up and solve Mitchell's 2D Elliptic Partial Differential Equations (PDE's) using the DEAL.II package.

Mitchell proposed these problems as a test suite for adaptive PDE solvers. An adaptive solver is one that constructs a proposed solution, estimates the error in this proposed solution, and then modifies its approach, perhaps by refining the mesh or using higher order elements, to reduce the error.

Licensing:

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

Related Data and Programs:

DEALII, examples which illustrate the use of DEAL.II, a finite element method (FEM) Differential Equations Analysis Library (DEAL), for the definition and solution of partial differential equations (PDE's), by Wolfgang Bangerth and others.

MITCHELL_FENICS, examples which illustrate the implementation of the Mitchell 2D elliptic partial differential equation (PDE) test problems using FENICS.

MITCHELL_FREEFEM++, examples which illustrate the implementation of the Mitchell 2D elliptic partial differential equation (PDE) test problems using FREEFEM++.

Author:

The DEAL.II implementations of these problems was done by Lukas Bystricky, of the Department of Scientific Computing, Florida State University.

Reference:

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

1. Wolfgang Bangerth, Ralf Hartmann, Guido Kanschat,
   DEAL.II - a general-purpose object-oriented finite element library,
   ACM Transactions on Mathematical Software,
   Volume 33, Number 4, article 24, August 2007.
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.

Examples and Tests:

Mitchell's problems include:

1. problem01, "Analytic solution".
2. problem02, "Reentrant Corner";
3. problem03, "Linear Elasticity";
4. problem04, "Peak";
5. problem05, "Battery";
6. problem06, "Boundary Layer";
7. problem07, "Boundary Line Singularity";
8. problem08, "Oscillatory";
9. problem09, "Wave Front";
10. problem10, "Interior Line Singularity";
11. problem11, "Intersecting Interfaces";
12. "Multiple Difficulties" (not implemented);

You can go up one level to the Examples directory.