, Volume 84, Issue 4, pp 527-548

Residual type a posteriori error estimates for elliptic obstacle problems

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Summary.

A posteriori error estimators of residual type are derived for piecewise linear finite element approximations to elliptic obstacle problems. An instrumental ingredient is a new interpolation operator which requires minimal regularity, exhibits optimal approximation properties and preserves positivity. Both upper and lower bounds are proved and their optimality is explored with several examples. Sharp a priori bounds for the a posteriori estimators are given, and extensions of the results to double obstacle problems are briefly discussed.

Received June 19, 1998 / Published online December 6, 1999