Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 0483400 (58 #3404a)
  • [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, 1965. MR 0209639 (35 #536)
  • [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.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N30, 76-08, 76E25

Retrieve articles in all journals with MSC: 65N30, 76-08, 76E25


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0669638-8
PII: S 0025-5718(1982)0669638-8
Article copyright: © Copyright 1982 American Mathematical Society