Error identities for variational problems with obstacles

This code illustrates new error identities for variational problems with obstacles. Identities define new measures, how to determine the distance of the approximation to the exact solutions of the nonlinear problem with obstacles respecting a free boundary.
There are three identities:
1) the primal error identity measuring the distance of primal variables (displacements).
2) the dual error identity measuring the distance of dual variables (fluxes)
3) the majorant identity measuring the combination of 1) and 2).
Only certain pertubations of exact solutions and corresponding exact fluxes are taken for simplicity as examples of approximation for testing. Thus, no approximations are computed numerically in this code.
Details on theory and numerics will be found in the forthcoming paper of Sergey Repin and Jan Valdman: Error identities for variational problems with obstacles. (submitted).
A link to the paper will be found at the author's web page http://sites.google.com/site/janvaldman/publications .
Please cite the paper if you find the code useful.
Call 'start' in the main directory to run the code.
By modifing parameters 'is_classical_obstacle' and 'is_1D', results for the classical obstacle problem (1D and 2D) and the two-phase obstacle problem (only 1D) are generated.