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Finite dimensional approximation of nonlinear problems. II: Limit points. (English) Zbl 0525.65036


MSC:

65J15 Numerical solutions to equations with nonlinear operators
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
35J65 Nonlinear boundary value problems for linear elliptic equations

Citations:

Zbl 0488.65021
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References:

[1] Berger, M.S.: Nonlinearity and functional analysis. New York: Academic Press, 1977 · Zbl 0368.47001
[2] Brezzi, F., Rappaz, J., Raviart, P.-A.: Finite dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions. Numer. Math.36, 1-25 (1980) · Zbl 0488.65021 · doi:10.1007/BF01395985
[3] Fujii, H., Yamaguti, M.: Structure of singularities and its numerical realization in nonlinear elasticity. J. Math. Kyoto (in press) (1981). · Zbl 0519.73078
[4] Girault, V., Raviart, P.-A.: An analysis of a mixed finite element method for the Navier-Stokes equations. Numer. Math.33, 235-271 (1979) · doi:10.1007/BF01398643
[5] Grisvard, P.: Singularité des solutions du problème de Stokes dans un polygone. Publication de I’Université de Nice (1978)
[6] Keller, H.B.: Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Applications of bifurcation theory. (P.H. Rabinowitz ed.), New York: Academic Press, pp. 359-384, 1977 · Zbl 0581.65043
[7] Kikuchi, F.: Numerical analysis of the finite element method applied to bifurcation problems of turning point type. ISAS Report no 564, University of Tokyo, 217-246 (1978)
[8] Kikuchi, F.: Finite element approximations to bifurcation problems of turning point type. Theoretical and Applied Mechanics27, 99-144 (1979) · Zbl 0416.65068
[9] Kikuchi, F.: Finite element approximation to bifurcation problems of turning point type. Troisième colloque international sur les méthodes de calcul scientifique et technique (Versailles 1977). Berlin Heidelberg New York: Springer 1981 (in press)
[10] Kondrat’ev, V.A.: Boundary value problems for elliptic equations in domains with canical and angular points. Trudy. Moskov. Mat. Ob??. 209-292 (1967)
[11] Paumier, J.C.: Une méthode numérique pour le calcul des points de retournement. Application au problème de Dirichlet ??u=?e u (in press) (1981)
[12] Scholz, R.: Finite element turning points of the Navier-Stokes equations. Conference on Progress in the Theory and Practice of the Finite Element Method. Chalmers University of Technology, Göteborg (1979)
[13] 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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