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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:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65J15Equations with nonlinear operators (numerical methods)
65N15Error bounds (BVP of PDE)
47J25Iterative procedures (nonlinear operator equations)
35J65Nonlinear boundary value problems for linear elliptic equations