Skip to main content
Article thumbnail
Location of Repository

Pointwise A Posteriori Error Analysis For An Adaptive Penalty Finite Element Method For The Obstacle Problem

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


. 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. 1. Introduction We consider finite element approximations of the obstacle problem \Gamma\Deltau(x) + fi(u(x) \Gamma /(x)) 3 f(x); x 2\Omega ; u(x) = 0; x 2 @\Omega ; (1.1) where / and f are given functions with / 0 on @ and where fi is the maximal monotone graph defined by fi(s) = 8 ? ! ? : f0g; s ? 0; (\Gamma1; 0]; s = 0; ;; s ! 0: (1.2) Our analysis and our finite element method are based on the following penalized (or regularized) form of (1.1): find u ffl such that \Gamma\Deltau ffl (x) + ffl(x) \Gamma1 (u ffl (x) \Gamma /(x)) \Gamma = f(x); x 2\Omega ; u ffl (x) = 0; x 2 @\Omega ; (1.3) w..

OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.