Donald A. French, Stig Larsson, and Ricardo H. Nochetto

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

Comput. Methods Appl. Math. 1 (2001), 18-38, 
http://www.emis.de/journals/CMAM

Abstract.  
  Finite element approximations based on a penalty formulation of the
  elliptic obstacle problem are analyzed in the maximum norm.  
  A posteriori 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.

Keywords. 
  elliptic obstacle problem, a posteriori error estimate,
  residual, maximum norm, adaptive, finite element, penalty method,
  duality argument 

Subject classification.  65N30, 35J85