Approximation of the spectrum of an operator given by the magnetohydrodynamic stability of a plasma

Jaccard, Yves; Evéquoz, Hugo

doi:10.1090/S0025-5718-1982-0669638-8

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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