Dr. Andreas Veeser
Diparimento di Matematica, Universita' di Milano
A posteriori error estimation, obstacles, and free boundaries.
Abstract: The obstacle problem for the Laplacian (Poisson's inequality) may be considered as a model problem for variational inequalities -- a class of problems that is ubiquitous in applications. This class is characterized by the appearance of an interface (free boundary) that seperates regions of different regimes and that is a priori unknown but often constitutes the "quantity of interest". In this talk, we propose a framework for the a posteriori error analysis of such problems and use it to derive estimators for the pointwise error of a finite element solution to Poisson's inequality. Furthermore, we construct a posteriori barrier sets for the exact free boundary. The practical impact of the derived estimators and barrier sets is illustrated by several numerical tests, also in 3d. This is joint work with Ricardo H. Nochetto (University of Maryland) and Kunibert G. Siebert (Universit"at Augsburg).
| Zeit: | Freitag, 21. November, 2003, 16.00 (Kaffee/Tee um 15.30 p.m.) |
| Ort: | FU Berlin, Arnimalle e 2-6, Raum 032 im EG |