On Mixed Error Estimates for Elliptic Obstacle Problems |
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Authors: | Liu Wenbin Ma Heping Tang Tao |
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Institution: | (1) Department of Mathematics, Xiang Tan University, Hunan Province, P.R. China;(2) CBS and Institute of Mathematics and Statistics, The University of Kent, Canterbury, CT2 7NF, England;(3) Department of Mathematics, Shanghai University, Shanghai, 200436, P.R.China;(4) Department of Mathematics, The Hong Kong Baptist University, Kowloon Tong, Hong Kong |
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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. |
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Keywords: | finite element approximation elliptic obstacle sharp a posteriori error estimates |
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