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Finite element approximation of a nonlinear eigenvalue problem related to MHD equilibria. (English) Zbl 0634.76117

This paper presents numerical analysis of finite element approximation to a nonlinear eigenvalue problem: \(-\Delta u=\lambda u^+\) in \(\Omega\), \(u=-1\) on \(\Gamma =\partial \Omega\), where \(\Omega\) is a bounded domain in \(R^ n(n=1,2,3)\). This problem arises in MHD equilibria and some other important physical phenomena. We consider a simple finite element scheme, and perform its error analysis. We also discuss a lumped finite element scheme, which is introduced to simplify the computations of the original scheme. Some numerical results are illustrated to show the validity of the analysis.

MSC:

76X05 Ionized gas flow in electromagnetic fields; plasmic flow
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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