Liu, W.B. and Yan, N. (2000) A Posteriori Error Estimators for a Class of Variational Inequalities. Journal of Scientific Computing, 15 (3). pp. 361-393. ISSN 0885-7474.
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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.
|Uncontrolled keywords:||Finite element approximation; variational inequalities; a posteriori error estimators; obstacle problems.|
|Subjects:||H Social Sciences > HA Statistics > HA33 Management Science|
|Divisions:||Faculties > Social Sciences > Kent Business School|
|Depositing User:||Steve Wenbin Liu|
|Date Deposited:||01 Jun 2009 07:02|
|Last Modified:||14 Jan 2010 14:31|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/8516 (The current URI for this page, for reference purposes)|
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