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Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem. (English) Zbl 0531.65061

See the preview in Zbl 0518.65081.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations

Citations:

Zbl 0518.65081
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References:

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[2] Bryan, C.A.: On the convergence of the method of nonlinear simultaneous displacements. Rend. Circ. Mat. Palermo13, 177-191 (1964) · Zbl 0133.37902 · doi:10.1007/BF02849526
[3] Ciarlet, P.G.: Discrete maximum principle for finite-difference operators. Aequationes Math.4, 338-352 (1970) · Zbl 0198.14601 · doi:10.1007/BF01844166
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[5] Dennis, J.E.: On Newton’s method and nonlinear simulatenous displacements. SIAM J. Numer. Anal.4, 103-108 (1967). · Zbl 0149.36502 · doi:10.1137/0704009
[6] Fujii, H.: Some remarks on finite element analysis of time-dependent field problems. In: Theory and practice in finite element structural analysis. Yamada, Y., Gallagher, R.H. (eds.) pp. 91-106. Univ. of Tokyo Press 1973
[7] Greenspan, D.: Introductory numerical analysis of elliptic boundary value problems. New York: Harper and Row 1965 · Zbl 0132.36602
[8] Ishihara, K.: On finite element schemes of the Dirichlet problem for a system of nonlinear elliptic equations. Numer. Funct. Anal. Optim.3, 105-136 (1981) · Zbl 0469.65071 · doi:10.1080/01630568108816081
[9] Ishihara, K.: Finite element approximations applied to the nonlinear boundary value problem ?u=bu 2. Publ. Res. Inst. Math. Sci.18, 17-34 (1982) · Zbl 0492.65062 · doi:10.2977/prims/1195184014
[10] Mimura, M.: Finite difference method for a class of semilinear parabolic system related to physical and biological problems. Doctoral Dissertation, Kyoto Univ. 1973
[11] Ortega, J.: Numerical analysis, a second course. New York: Academic Press 1972 · Zbl 0248.65001
[12] Ortega, J., Rheinboldt, W.: Iterative solution of nonlinear equations in several variables. New York: Academic Press 1970 · Zbl 0241.65046
[13] Osher, S.: Nonlinear singular perturbation problems and one sided difference schemes. SIAM J. Numer. Anal.18, 129-144 (1981) · Zbl 0471.65069 · doi:10.1137/0718010
[14] Osher, S.: Approximation par éléments finis avec décentrage de problémes de perturbations singuliéres quasi linéaires et multidimensionnels. C.R. Acad. Sci. Paris Ser. I292, 99-101 (1981) · Zbl 0471.65070
[15] Pohozaev, S.I.: The Dirichlet problem for the equation ?u=u 2. Soviet Math. Dokl.1, 1143-1146 (1960) · Zbl 0097.08503
[16] Rall, L.: Computational solution of nonlinear operator equations. New York: John Wiley 1969 · Zbl 0175.15804
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[18] Varga, R.: Matrix iterative analysis. Englewood Cliffs, N.J.: Prentice-Hall 1962 · Zbl 0133.08602
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