On Mixed Error Estimates for Elliptic Obstacle Problems
Source: Advances in Computational Mathematics, Volume 15, Numbers 1-4, November 2001 , pp. 261-283(23)
Abstract:We establish in this paper sharp error estimates of residual type for finite 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 a posteriori error indicators reliable and efficient up to higher order terms, and these indicators are useful in mesh-refinements and adaptive grid generations. In particular, by approximating the a priori part with some a posteriori quantities we can successfully track the free boundary for elliptic obstacle problems.
Document Type: Regular Paper
Affiliations: 1: CBS and Institute of Mathematics and Statistics, The University of Kent, Canterbury, CT2 7NF England E-mail: email@example.com 2: Department of Mathematics, Shanghai University, Shanghai 200436, P.R. China E-mail: firstname.lastname@example.org 3: Department of Mathematics, The Hong Kong Baptist University, Kowloon Tong, Hong Kong E-mail: email@example.com
Publication date: November 1, 2001