Approximation of the spectrum of an operator given by the magnetohydrodynamic stability of a plasma
Authors:
Yves Jaccard and Hugo Evéquoz
Journal:
Math. Comp. 39 (1982), 443-452
MSC:
Primary 65N30; Secondary 76-08, 76E25
DOI:
https://doi.org/10.1090/S0025-5718-1982-0669638-8
MathSciNet review:
669638
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Abstract: The study of the magnetohydrodynamic (MHD) stability of a plasma in a toroidal configuration leads to a problem of computing the spectrum of a noncompact selfadjoint operator T. The spectrum of T will be approximated by the eigenvalues of ${T_h}$, a Galerkin approximation of T. We present a two-dimensional model problem with two components containing most difficulties arising in the physical problem. We give subspaces and prove sufficient conditions for obtaining convergence using partial regularity of T.
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D. Berger, Numerical Computations of the Ideal Magnetohydrodynamic Stability of Small Aspect Ratio Tokamaks, Thesis No 131, EPF-Lausanne, 1977.
- Jean Descloux, Nabil Nassif, and Jacques Rappaz, On spectral approximation. I. The problem of convergence, RAIRO Anal. Numér. 12 (1978), no. 2, 97–112, iii (English, with French summary). MR 483400, DOI https://doi.org/10.1051/m2an/1978120200971 H. Evéquoz, Approximation Spectrale d’un Opérateur Lié à l’Étude de la Stabilité Magnétohydrodynamique d’un Plasma par une Méthode d’ Éléments Finis Non Conforme, Thesis No 375, EPF-Lausanne, 1980.
- Gaetano Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, vol. 8, Springer-Verlag, Berlin-New York, 1965. MR 0209639 R. Gruber, Numerical Computations of the Magnetohydrodynamic Spectrum for One and Two Dimensional Equilibria Using Regular Finite Elements and Finite Hybrid Elements, Thesis No 246, EPF-Lausanne, 1976. Y. Jaccard, Approximation Spectrale par la Méthode des Éléments Finis Conformes d’une Classe d’Opérateurs Non Compacts et Partiellement Réguliers, Thesis No 374, EPF-Lausanne, 1980. N. Krall & A. Trivelpiece, Principles of Plasma Physics, McGraw-Hill, New York, 1973. J. Rappaz, Approximation par la Méthode des Éléments Finis du Spectre d’un Opérateur Non Compact Donné par la Stabilité Magnétohydrodynamique d’un Plasma, Thesis No 239, EPF-Lausanne, 1976.
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Article copyright:
© Copyright 1982
American Mathematical Society