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.