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Une méthode numérique pour le calcul des points de retournement. Application à un problème aux limites non-linéaire. II: Analyse numérique d’un problème aux limites non-linéaire. (French) Zbl 0449.65025


MSC:

65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
65H10 Numerical computation of solutions to systems of equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs

Citations:

Zbl 0449.65024
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References:

[1] Adams, R.A.: Sobolev Spaces. New York: Academic Press 1975 · Zbl 0314.46030
[2] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. Siam Rev.18, 620-709 (1976) · Zbl 0345.47044 · doi:10.1137/1018114
[3] Brezzi, F., Rappaz, J., Raviart, P.A.: Finite dimensional approximation of nonlinear problems. Part 2: limit points. Numer. Math.37, 1-28 (1981) · Zbl 0525.65036 · doi:10.1007/BF01396184
[4] Ciarlet, P.G.: The finite Element Method for Elliptic Problems. North Holland 1978 · Zbl 0383.65058
[5] Crandall, M.G., Rabinowitz, P.H.: Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems. Arch. Rat. Mech. Anal.58, 207-218 (1975) · Zbl 0309.35057 · doi:10.1007/BF00280741
[6] Grisvard, P.: Behaviour of the solution of an elliptic boundary value problem in a polygonal or polyhedral domain, numerical solution of partial differential equations, III, Synspade 1975, Ed. Hubbard, Acad. Press 204-274 (1976)
[7] Kikuchi, F.: Finite element approximations to bifurcation problems of turing point type. Comptes-rendus du Troisième Colloque International sur les Méthodes de Calcul Scientifique et Technique, I.R.I.A., Versailles-Rocquencourt 1977
[8] Mignot, F., Puel, J.P.: Sur une classe de problèmes non lineaires avec non linéarité positive, croissante, convexe; Université Pierre et Marie Curie, Laboratoire d’Analyse Numérique (L.A. 189), Rapport interne no 78028 1978 · Zbl 0404.35049
[9] Paumier, J.C.: Une méthode numérique pour le calcul des points de retournement. Application à un problème aux limites non linéaire, I. Etude théorique et expérimentation de la méthode. Numer. Math.37, 433-444 (1981) · Zbl 0449.65024 · doi:10.1007/BF01400320
[10] Simpson, R.B.: Existence and error estimates for solutions of a discrete analog of nonlinear eigenvalue problems. Math. Comput.26, 359-375 (1972) · Zbl 0256.65048 · doi:10.1090/S0025-5718-1972-0315918-9
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