On Mixed Error Estimates for Elliptic Obstacle Problems

In this paper, we establish sharp error estimates of residual type for nite element approximation to elliptic obstacle problems. The estimates are of mixed nature, which are neither of a pure a priori form nor of a pure a posteriori form but instead they are combined by an a priori part and an a posteriori part. The key ingredient in our derivation for the mixed error estimates is the use of a new interpolator which enables us to eliminate inactive data from the error estimators. One application of our mixed error estimates is to construct reliable and eecient a posteriori error indicators useful in mesh-reenements and adaptive grid generations. In particular, by approximating the a priori part with some a posteriori quantities we can successfully track the free boundary of elliptic obstacle problems.