Numerische Mathematik

, Volume 95, Issue 1, pp 163–195 | Cite as

Pointwise a posteriori error control for elliptic obstacle problems

  • Ricardo H. Nochetto
  • Kunibert G. Siebert
  • Andreas Veeser
Article

Abstract

We consider a finite element method for the elliptic obstacle problem over polyhedral domains in ℝ d , 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ricardo H. Nochetto
    • 1
  • Kunibert G. Siebert
    • 2
  • Andreas Veeser
    • 3
  1. 1.Department of Mathematics and Institute of Physical Science and TechnologyUniversity of MarylandCollege ParkUSA
  2. 2.Institut für Angewandte MathematikFreiburgGermany
  3. 3.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly

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