Gatica, Gabriel N.; Heuer, Norbert; Meddahi, Salim On the numerical analysis of nonlinear twofold saddle point problems. (English) Zbl 1028.65128 IMA J. Numer. Anal. 23, No. 2, 301-330 (2003). 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. Reviewer: Pavol Chocholatý (Bratislava) Cited in 41 Documents 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 Keywords:Galerkin method; nonlinear operator equation; nonlinear twofold saddle point problem; nonlinear elliptic problem; numerical results Citations:Zbl 1024.65044; Zbl 0992.74068 PDFBibTeX XMLCite \textit{G. N. Gatica} et al., IMA J. Numer. Anal. 23, No. 2, 301--330 (2003; Zbl 1028.65128) Full Text: DOI Link