A posteriori error estimator for obstacle problems
Project description
In this project, we consider error estimators for obstacle problems.
The focus is on error estimators which are defined in terms of H(div) conforming stress
approximations and equilibrated fluxes.
It can be shown that the error is bounded by the estimator with a constant one
plus a higher order data oscillation term plus a term arising from the contact
that is shown numerically to be of higher order.
Moreover bounds for the Lagrange multiplier and efficiency of the estimator are
derived.

Problem with exact solution, error
decay and ration between estimated and exact error 

Problem with exact solution: grid at
level 2,4,6, active nodes and exact contact set (red) 
For the case of nonsmooth or discontinuous obstacles, suitable
modifications in the estimator are considered. Here, the H(div) conformity must
be weakend as the exact solution is no longer H(div) conform.
The estimator has been implemented and applied to various examples including
twomembrane contact problem problem with
nonmatching meshes and low regularity problems.
Optimal convergence is achieved using adaptive mesh refinement.

Low regularity problem: Setting and
solution for alpha=pi/6 and alpha=pi/2 

Low regularity problem: Optimal
convergence by adaptive refinement 

Twomembrane + obstacle problem: Setting and solution


Twomembrane + obstacle problem: Grid and active sets at level 3,6,9.

Publications
Author(s) 
Title 
Appeared In 
Year 
Type 
Download 
Alexander Weiss, Barbara Wohlmuth 
A Posteriori Error Estimator for Obstacle Problems 
SIAM J. Sci. Comput. 32, no. 5, 2627–2658 
2010 
Article in Journal 
Abstract
Link ^{}
Bibtex
