A posteriori error estimation and adaptive solution of elliptic variational inequalities of the second kind

In this paper, we perform an a posteriori error analysis for adaptive finite element solutions of elliptic variational inequalities of the second kind. A general framework for a posteriori error estimates is established by using duality theory in convex analysis. We then turn to an analysis of some...

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Bibliographic Details
Published in:Applied numerical mathematics 2005, Vol.52 (1), p.13-38
Main Authors: Bostan, Viorel, Han, Weimin, Reddy, B.D.
Format: Article
Language:English
Subjects:
A posteriori error estimation
Adaptive finite element solution
Calculus of variations and optimal control
Duality
Efficiency
Elliptic variational inequality
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Sciences and techniques of general use
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Summary:In this paper, we perform an a posteriori error analysis for adaptive finite element solutions of elliptic variational inequalities of the second kind. A general framework for a posteriori error estimates is established by using duality theory in convex analysis. We then turn to an analysis of some particular a posteriori error estimates of residual type. Efficiency of the error estimators are investigated. Numerous numerical examples are included to illustrate the effectiveness of the a posteriori error estimates in adaptive solutions of the variational inequalities.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2004.06.012