01-2   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Sören Bartels, Carsten Carstensen:

Averaging Techniques Yield Reliable A Posteriori Finite Element Error Control for Obstacle Problems

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.

Mathematics Subject Classification (1991): 65N30, 65R20, 73C50

Keywords: Adaptive finite element methods, a posteriori error estimates, elliptic variational inequalities, obstacle problems


Mail an Jens Burmeister
[Thu Feb 19 18:56:35 2009]
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