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Finite dimensional approximation of nonlinear problems. III: Simple bifurcation points. (English) Zbl 0525.65037


MSC:

65J15 Numerical solutions to equations with nonlinear operators
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76G25 General aerodynamics and subsonic flows
35J65 Nonlinear boundary value problems for linear elliptic equations
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References:

[1] Babuska, I., Osborn, J., Pitkäranta, J.: Analysis of mixed methods using mesh dependent norms. MRC Rech. Summary Report # 2003 (1979), University of Wisconsin, Madison
[2] Berger, M.S.: Nonlinearity and functional analysis. New York: Academic Press 1977 · Zbl 0368.47001
[3] Bernardi, C.: Approximation of Hopf bifurcation. Numer. Math. (in press, 1981) · Zbl 0456.65033
[4] 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
[5] Brezzi, F., Rappaz, J., Raviart, P.-A.: Finite-dimensional approximation of nonlinear problems. Part II: Limit points. Numer. Math.37, 1-28 (1981) · Zbl 0525.65036 · doi:10.1007/BF01396184
[6] Brezzi, F., Raviart, P.-A.: Mixed finite element methods for 4th order elliptic equations. Topics in numerical analysis II (J.J.H. Miller ed.), pp. 33-56. London: Academic Press 1976
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[9] Girault, V., Raviart, P.-A.: An analysis of some upwind schemes for the Navier-Stokes equations SIAM. J. Numer. Anal. (in press) · Zbl 0487.76036
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[11] Herrmann, L.R.: A bending analysis for plates. Proc. Conf. on Matrix Methods in Structural Mechanics, AFFDL-TR-66-88, 577-604
[12] Johnson, C.: On the convergence of a mixed finite element method for plate bending problems. Numer. Math.21, 43-62 (1973) · Zbl 0264.65070 · doi:10.1007/BF01436186
[13] Keller, H.B.: (To appear)
[14] Kesavan, S.: La méthode de Kikuchi appliquée aux équations de van Kármán. Numer. Math.32, 209-232 (1979) · Zbl 0395.73054 · doi:10.1007/BF01404876
[15] Kesavan, S.: Une méthode d’éléments finis mixte pour les équations de von Kármán. RAIRO Numer. Anal.14, 149-173 (1980) · Zbl 0451.73053
[16] Kikuchi, F.: An iterative finite element scheme for bifurcation analysis of semilinear elliptic equations. Report Inst. Space. Aero. Sc. # 542 (1976), Tokyo University
[17] Nirenberg, L.: Topics in nonlinear functional Analysis. Courant Institute of Mathematical Science, New York University (1974) · Zbl 0286.47037
[18] Rappaz, J., Raugel, G.: Finite-dimensional approximation of bifurcation problems at a double eigenvalue. (To appear) · Zbl 0571.65048
[19] Raugel, G.: (To appear)
[20] Sattinger, D.H.: Group theoretic methods in bifurcation theory. Lecture Notes in Mathematics Vol. 762. Berlin Heidelberg New York: Springer 1979 · Zbl 0414.58013
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