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Brezzi, F.; Rappaz, J.; Raviart, P. A.

Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions. (English) Zbl 0488.65021

Numer. Math. 36, 1-25 (1980).
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Cited in 17 Reviews
Cited in 169 Documents

MSC:

65J15 Numerical solutions to equations with nonlinear operators
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
47J25 Iterative procedures involving nonlinear operators
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q99 Partial differential equations of mathematical physics and other areas of application
74K20 Plates

Keywords:

mixed finite-element methods; Banach space; implicit function theorem; continuation methods; convergence in a parameter; von Kármán equations
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\textit{F. Brezzi} et al., Numer. Math. 36, 1--25 (1980; Zbl 0488.65021)
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References:

[1] Brezzi, F., Fujii, H.: Mixed finite element approximations of the Von Kármán equations. Proceedings of the 4th L1BLICE Conference on Basic Problems of Numerical Analysis, Pilsen, Czechoslovakia, September 1978 · Zbl 0444.73060
[2] Brezzi, F., Raviart, P-A: Mixed finite element methods for 4th order elliptic equations. Topics in Numerical Analysis III (J.J.H. Miller, ed.), pp. 33-56. London: Academic Press 1976
[3] Falk, R.S., Osborn, J.E.: Error estimates for mixed methods. R.A.I.R.O. Numer. Anal. (in press, 1980) · Zbl 0467.65062
[4] Fujii, H., Yamaguti, M.: Structure of singularities and its numerical realization in nonlinear elasticity, Research Report KSU/ICS 78-06, Kyoto Sangyo University · Zbl 0519.73078
[5] Girault, V., Raviart, P-A: Finite element approximation of the Navier-Stokes equations. Lecture Notes in Mathematics, No. 749. Heidelberg, New York: Springer 1979 · Zbl 0413.65081
[6] Girault, V., Raviart, P-A: An analysis of a mixed finite element methods for the Navier-Stokes equations. Numer. Math.33, 235-271 (1979) · Zbl 0414.65068
[7] Girault, V., Raviart, P-A.: An analysis of an upwind scheme for the Navier-Stokes equations. (in press, 1980) · Zbl 0487.76036
[8] Grisvard, P.: Singularité des solutions du problème de Stokes dans un polygone. Publications de l’Université de Nice (1978)
[9] Keller, H.B.: Approximation methods for nonlinear problems with applications to two-point boundary value problems. Math. Comput.29, 464-474 (1975) · Zbl 0308.65039
[10] Kondrat’ev, V.A.: Boundary value problems for elliptic equations in domains with conical and angular points. Trudy Moskov. Mat. Ob??.16, 209-292 (1967)
[11] Lions, J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod 1969
[12] Raviart, P-A: On the finite element approximation of nonlinear, problems. Computational methods in nonlinear mechanics (J.T. Oden ed.), pp. 413-425. Amsterdam: North-Holland 1980
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