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Approximation of the spectrum of a non-compact operator given by the magnetohydrodynamic stability of a plasma. (English) Zbl 0341.65044

MSC:
65J05 General theory of numerical analysis in abstract spaces
76W05 Magnetohydrodynamics and electrohydrodynamics
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[1] Appert, K., Berger, D., Gruber, R., Rappaz, J., Troyon, F.: Studium der Eigenschwingungen eines zylindrischen Plasmas mit der Methode der finiten Elemente. ZAMP25, 229-340 (1974) · Zbl 0282.76088 · doi:10.1007/BF01591323
[2] Appert, K., Berger, D., Gruber, R., Rappaz, J.: A new finite element approach to the normal mode analysis in magnetohydrocdynamics. Comput. Phys.18, 284-299 (1975) · Zbl 0319.76038 · doi:10.1016/0021-9991(75)90003-0
[3] Babuska, I., Aziz, A.K.: Survey lectures on the mathematical foundations of the finite element method (A.K. Aziz, ed.). New York-London: Academic Press 1972
[4] Bramble, J.H., Osborn, J.E.: Rate of convergence estimates for non-selfadjoint eigenvalue approximations. MCR Tech. Sum. Rep. 1232, June 1972 · Zbl 0305.65064
[5] Bramble, J.H., Osborn, J.E.: Approximation of Steklov eigenvalues of non-selfadjoint second order elliptic operator (A.K. Aziz, ed.). New York-London: Academic Press 1972 · Zbl 0264.35055
[6] Chatelin, F.: Convergence of approximation methods to compute eigenelements of linear operations. SIAM J. Numer. Anal.10, No. 5, 939-948 (1973) · Zbl 0266.65048 · doi:10.1137/0710080
[7] Gruber, R.: Numerical computations of the magnetohydrodynamic spectrum for one and two dimensional equilibria using regular finite elements and finite hybrid elements. Thèse EPFL, Département de physique, April 1976
[8] Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0148.12601
[9] Rappaz, J.: Approximation par la méthode des éléments finis du spectre d’un opérateur non compact donné par la stabilité magnétohydrodynamique d’un plasma. Thèse EPFL, Département de Mathématiques, avril 1976
[10] Riesz, F., Nagy, B.S.Z.: Leçon d’analyse fonctionelle, 6e ed. Budapest: Gauthier-Villars 1972
[11] Strang, G., Fix, G.J.: An analysis of the finite element method. Englewood Cliffs, N.J.: Prentice-Hall 1973 · Zbl 0356.65096
[12] Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1965 · Zbl 0126.11504
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