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.


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


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



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.