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.


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