Title:

Numerical Methods for obstacle problems

Abstract:

An obstacle problem can be written in the form of a variational inequality or as a minimization problem of the Dirichlet functional. Typically, the obstacle is included in the function space, but I will also present the possibility to include the obstacle through a penalty term.

With the Lemma of Zarantonello it follows that the penalized problem has a unique solution and that is converges to the original solution if the penalty parameter converges to zero.

The problem is then discretized and the error is estimated by a generalization of the Lemma of Cea.

Then we look at some examples, where we compare the convergence and iteration numbers of different algorithms.

Gabriele Dürnberger
(NuMa)

Date: Tuesday, Apr 8, 2025
Time: 4:15 pm, S2 059