A Posteriori Error Estimators for a Class of Variational Inequalities

Authors:
Wenbin Liu;Ningning Yan
Affiliations:
CBS & Institute of Mathematics and Statistics, University of Kent, Canterbury, CT2 7NF, England;Institute of Systems Science, Academia Sinica, Beijing 100080, People's Republic of China
Venue:
Journal of Scientific Computing
Year:
2000

Citing 4
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Abstract

In this paper, we present an a posteriori error analysis for the finite element approximation of a variational inequality. We derive a posteriori error estimators of residual type, which are shown to provide upper bounds on the discretization error for a class of variational inequalities provided the solutions are sufficiently regular. Furthermore we derive sharp a posteriori error estimators with both lower and upper error bounds for a subclass of the obstacle problem which are frequently met in many physical models. For sufficiently regular solutions, these estimates are shown to be equivalent to the discretization error in an energy type norm. Our numerical tests show that these sharp error estimators are both reliable and efficient in guiding mesh adaptivity for computing the free boundaries.