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Approximation of a nondifferentiable nonlinear problem related to MHD equilibria. (English) Zbl 0527.65073


MSC:

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
35P15 Estimates of eigenvalues in context of PDEs
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References:

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[2] Ciarlet, P.G.: The finite element method for elliptic problems. Studies in Math. and Its Appl. Amsterdam: North-Holland, 1978
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[5] Girault, V., Raviart, P.A.: An analysis of upwind schemes for the Navier-Stokes equations. SIAM. J. Numer. Anal.19, 312-333 (1982) · Zbl 0487.76036 · doi:10.1137/0719019
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[8] Kikuchi, F.: Construction of a path of MHD equilibrium solutions by an iterative method. Institute of Space and Aeronautical Science University of Tokyo, Report No 574, pp. 97-111, 1979
[9] Osborn, J.E.: Spectral approximation for compact operators. Math. Comput.29, 712-725 (1975) · Zbl 0315.35068 · doi:10.1090/S0025-5718-1975-0383117-3
[10] Puel, J.P.: A free boundary, nonlinear eigenvalue problem, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations. De la Penha, Medeiros (eds.), Amsterdam: North-Holland, pp. 400-410, 1978
[11] Sermange, M.: Etude math?matique et num?rique de probl?mes aux limites non lin?aires intervenant en physique des plasmas. Th?se d’Etat, Universit? Paris XI, 1982
[12] Temam, R.: A nonlinear eigenvalue problem: the shape of equilibrium of a confined plasma. Arch. Rational Mech. Anal.60, 51-73 (1975) · Zbl 0328.35069 · doi:10.1007/BF00281469
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