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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: Finite element analysis of a nondifferentiable nonlinear problem related to MHD equilibria
著者: Kikuchi, Fumio
キーワード: Newton-like methods
finite element method
発行日: 1988年
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, Section IA, Mathematics, Vol.35(1988), No.1, Page 77-101
抄録: (Summary) We consider finite element approximation of a nondifferentiable nonlinear eigenvalue problem related to MHD (magnetohydrodynamics) equilibria. In an abstract setting, we first present two Newton-like iteration schemes as generalizations of the usual Newton method and the modified Newton method, and consider their convergence properties with an implicit function theorem derived. Then we apply the results to a nonlinear eigenvalue problem described by a semilinear elliptic problem with a nondifferentiable nonlinear term. Finally, we introduce a simple finite element model to this problem, to which we show that the iteration schemes are applicable. Order estimates of the errors of the finite element solutions are also given under some assumptions. A few numerical results are illustrated to see the validity of the analysis.
URI: http://hdl.handle.net/2261/1683
ISSN: 00408980
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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