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

Carsten Carstensen and S. Bartels

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Submission date: 29. Jan. 2001
Pages: 22
published in: Numerische Mathematik, 99 (2004) 2, p. 225-249 
DOI number (of the published article): 10.1007/s00211-004-0553-6
Bibtex
MSC-Numbers: 65N30, 65R20, 73C50
Keywords and phrases: adaptative finite element methods, a posteriori error estimates, elliptic variational inequalities, obstacle problems
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Abstract:
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.