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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
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.

References [Enhancements On Off] (What's this?)

  • [1] D. Berger, Numerical Computations of the Ideal Magnetohydrodynamic Stability of Small Aspect Ratio Tokamaks, Thesis No 131, EPF-Lausanne, 1977.
  • [2] 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,
  • [3] 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.
  • [4] Gaetano Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, vol. 8, Springer-Verlag, Berlin-New York, 1965. MR 0209639
  • [5] 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.
  • [6] 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.
  • [7] N. Krall & A. Trivelpiece, Principles of Plasma Physics, McGraw-Hill, New York, 1973.
  • [8] 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