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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Error estimates for the approximation of a class of variational inequalities

Author: Richard S. Falk
Journal: Math. Comp. 28 (1974), 963-971
MSC: Primary 65K05; Secondary 35J30
MathSciNet review: 0391502
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Abstract: In this paper, we prove a general approximation theorem useful in obtaining order of convergence estimates for the approximation of the solutions of a class of variational inequalities. The theorem is then applied to obtain an "optimal" rate of convergence for the approximation of a second-order elliptic problem with convex set $K = \{ \upsilon \in H_0^1(\Omega ):\upsilon \geqslant \chi$ a.e. in $\Omega$}.

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Article copyright: © Copyright 1974 American Mathematical Society