Numerische Mathematik

, Volume 99, Issue 2, pp 225–249

Averaging techniques yield reliable a posteriori finite element error control for obstacle problems

Article

DOI: 10.1007/s00211-004-0553-6

Cite this article as:
Bartels, S. & Carstensen, C. Numer. Math. (2004) 99: 225. doi:10.1007/s00211-004-0553-6

Summary.

The reliability of frequently applied averaging techniques for a posteriori error control has recently been established for a series of finite element methods in the context of second-order partial differential equations. This paper establishes related reliable and efficient a posteriori error estimates for the energy-norm error of an obstacle problem on unstructured grids as a model example for variational inequalities. The surprising main result asserts that the distance of the piecewise constant discrete gradient to any continuous piecewise affine approximation is a reliable upper error bound up to known higher order terms, consistency terms, and a multiplicative constant.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsHumboldt-Universität zu BerlinBerlinGermany

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