Projection/fixed point method for solving a semilinear obstacle problem

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 cont...

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Published inInternational journal of computer mathematics Vol. 98; no. 5; pp. 999 - 1014
Main Authors Mellah, Zhor, Bekkaye Mermri, El
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2021
Taylor & Francis Ltd
Subjects
Algorithms
approximation
Barriers
Continuity (mathematics)
Finite element method
numerical method
obstacle problem
semilinear
Variational inequality
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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.
AbstractList 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.
Author Mellah, Zhor
Bekkaye Mermri, El
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10.1007/978-3-662-12613-4
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StartPage 999
SubjectTerms Algorithms
approximation
Barriers
Continuity (mathematics)
Finite element method
numerical method
obstacle problem
semilinear
Variational inequality
Title Projection/fixed point method for solving a semilinear obstacle problem
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