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Original Articles

Projection/fixed point method for solving a semilinear obstacle problem

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Pages 999-1014 | Received 24 Jan 2020, Accepted 21 Jul 2020, Published online: 18 Aug 2020
 

Abstract

In this paper, we present a reformulation of a unilateral semilinear obstacle problem as a projection/fixed point problem based on appropriate variational inequality of the second kind and the subdifferential μ of a convex continuous function. The function μ leads to the characterization of the contact domain. Then we present the algorithms to solve the reformulated problem. We approximate the continuous problem by finite element method, then we present the analysis of the discrete problem and prove the convergence of the approximate solutions to the exact one.

2010 Mathematics Subject Classifications:

Acknowledgments

We thank two anonymous referees for carefully reading the first version of the paper and for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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