Residual type a posteriori error estimates for elliptic obstacle problems

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