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On the numerical analysis of nonlinear twofold saddle point problems
Authors:Gatica, Gabriel N.   Heuer, Norbert   Meddahi, Salim
Affiliation: 1 GI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile 2 Departamento de Matemática, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo, España
Abstract:We provide a general abstract theory for the solvability andGalerkin approximation of nonlinear twofold saddle point problems.In particular, a Strang error estimate containing the consistencyterms arising from the approximation of the continuous operatorsinvolved is deduced. Then we apply these results to analysea fully discrete Galerkin scheme for a twofold saddle pointformulation of a nonlinear elliptic boundary value problem indivergence form. Some numerical results are also presented.
Keywords:Dual–  dual formulation   nonlinear operator equation   fully discrete scheme   numerical quadrature
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