Finite element analysis of a nondifferentiable nonlinear problem related to MHD equilibria
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概要
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(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.
- Faculty of Science, The University of Tokyoの論文
Faculty of Science, The University of Tokyo | 論文
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