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


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
Full Text: DOI EuDML


[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) · doi:10.1007/BF01398643
[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 · doi:10.1090/S0025-5718-1975-0371058-7
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.