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Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics >

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タイトル: An abstract analysis of parameter dependent problems and its applications to mixed finite element methods
著者: Kikuchi, Fumio
キーワード: Mixed finite element method
Parameter dependent problem
Penalty approach
Iteration scheme
Locking
発行日: 1985年12月25日
出版者: Faculty of Science, The University of Tokyo
掲載誌情報: Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics, Vol.32(1985), No.3, Page499-538
抄録: This paper is concerned with numerical analysis of a class of parameter dependent problems. Such problems arise, for example, from the analysis of nearly incompressible media and from the penalization of some constrained minimization problems. We first consider the solvability and the uniqueness of an abstract problem under certain hypotheses, and then analyze the dependence of the solutions on the parameter. We also propose an iteration scheme, by which we can obtain solutions for fairly wide range of parameter values. We introduce a mixed finite element approximation to the present problem, and discuss its approximation properties. In particular, we consider the locking phenomenon, which often arises from numerical approximation of the present type of problems. We also give some simple numerical results to see the dependence of numerical solutions on the parameter. In Appendices, we present some sufficient conditions for the hypotheses employed to assure the solvability of the present problem and its approximations.
URI: http://hdl.handle.net/2261/6426
ISSN: 0040-8980
出現カテゴリ:Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics
Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics

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