Pointwise A Posteriori Error Analysis for an Adaptive Penalty Finite Element Method for the Obstacle Problem

Comput. Methods Appl. Math., 1 (2001), 18-38.

Donald A.~French
Department of Mathematical Sciences
University of Cincinnati
Cincinnati, Ohio 45221, USA


Stig Larsson
Department of Mathematics
Chalmers University of Technology and G\"oteborg University
SE--412 96 G\"oteborg, Sweden


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



Finite element approximations based on a penalty formulation of the obstacle problem are analyzed in the maximum norm. {\Aposteriori} error estimates, which involve a residual of the approximation and a spatially variable penalty parameter, are derived in the cases of both smooth and rough obstacles. An adaptive algorithm is suggested and implemented in one dimension.