On the numerical analysis of nonlinear twofold saddle point problems
Gabriel N. Gatica, Norbert Heuer, Salim Meddahi
IMA J. Numer. Anal. 23 (2), 301-330, 2003.
We provide a general abstract theory for the solvability and Galerkin
approximations of nonlinear two-fold saddle point problems.
In particular, a Strang error estimate containing the consistency terms
arising from the approximation of the continuous operators involved is deduced.
Then we apply these results to analyze a fully discrete Galerkin scheme for a
two-fold saddle point formulation of a nonlinear elliptic boundary value
problem in divergence form. Some numerical results are also presented.