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On the numerical analysis of nonlinear twofold saddle point problems. (English) Zbl 1028.65128

The purpose of this paper is to unify the main results of [G. N. Gatica, Z. Anal. Anwend. 21, No. 3, 761-781 (2002; Zbl 1024.65044)] and of [G. N. Gatica and N. Heuer, SIAM J. Numer. Anal. 38, No. 2, 380-400 (2000; Zbl 0992.74068)] and to provide a complete and general theory for solvability and Galerkin approximations of the nonlinear twofold saddle point problem. Then, an application of this theory to a nonlinear elliptic problem in divergence form is described. Also several numerical results are presented.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65J15 Numerical solutions to equations with nonlinear operators
65N15 Error bounds for boundary value problems involving PDEs
47J25 Iterative procedures involving nonlinear operators
35J65 Nonlinear boundary value problems for linear elliptic equations
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