Numerische Mathematik

, Volume 95, Issue 1, pp 163–195

Pointwise a posteriori error control for elliptic obstacle problems

Authors

    • Department of Mathematics and Institute of Physical Science and TechnologyUniversity of Maryland
  • Kunibert G. Siebert
    • Institut für Angewandte Mathematik
  • Andreas Veeser
    • Dipartimento di MatematicaUniversità degli Studi di Milano
Article

DOI: 10.1007/s00211-002-0411-3

Cite this article as:
Nochetto, R., Siebert, K. & Veeser, A. Numer. Math. (2003) 95: 163. doi:10.1007/s00211-002-0411-3

Abstract

We consider a finite element method for the elliptic obstacle problem over polyhedral domains in ℝd, which enforces the unilateral constraint solely at the nodes. We derive novel optimal upper and lower a posteriori error bounds in the maximum norm irrespective of mesh fineness and the regularity of the obstacle, which is just assumed to be Hölder continuous. They exhibit optimal order and localization to the non-contact set. We illustrate these results with simulations in 2d and 3d showing the impact of localization in mesh grading within the contact set along with quasi-optimal meshes.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002