Residual type a posteriori error estimates for elliptic obstacle problems
- Cite this article as:
- Chen, Z. & Nochetto, R. Numer. Math. (2000) 84: 527. doi:10.1007/s002110050009
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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.