Fully Localized A~posteriori Error Estimators and Barrier Sets for Contact Problems

Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA.

rhn@math.umd.edu

Kunibert G. Siebert
Institut fuer Mathematik
Universitaet Augsburg
D-86159 Augsburg, Germany.

siebert@math.uni-augsburg.de

Andreas Veeser
Dipartimento di Matematica
Universit\`a degli Studi di Milano
20133 Milano, Italy.

andreas.veeser@mat.unimi.it

Abstract

We derive novel pointwise a posteriori error estimators for elliptic obstacle problems which, except for obstacle resolution, completely vanish within the full-contact set (localization). We then construct a~posteriori barrier sets for free boundaries under a natural stability (or nondegeneracy) condition. We illustrate localization properties as well as reliability and efficiency for both solutions and free boundaries via several simulations in 2d and 3d.