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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
2/2001

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

Carsten Carstensen and S. Bartels

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.

Received:
Jan 29, 2001
Published:
Jan 29, 2001
MSC Codes:
65N30, 65R20, 73C50
Keywords:
adaptative finite element methods, a posteriori error estimates, elliptic variational inequalities, obstacle problems

Related publications

inJournal
2004 Repository Open Access
S. Bartels and Carsten Carstensen

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

In: Numerische Mathematik, 99 (2004) 2, pp. 225-249