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IMA Journal of Numerical Analysis 2003 23(2):301-330; doi:10.1093/imanum/23.2.301
© 2003 by Institute of Mathematics and its Applications
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On the numerical analysis of nonlinear twofold saddle point problems

Gabriel N. Gatica1, Norbert Heuer1 and Salim Meddahi2

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

We provide a general abstract theory for the solvability and Galerkin approximation of nonlinear twofold 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 analyse a fully discrete Galerkin scheme for a twofold saddle point formulation of a nonlinear elliptic boundary value problem in divergence form. Some numerical results are also presented.

Key Words: Dual–dual formulation; nonlinear operator equation; fully discrete scheme; numerical quadrature

Received 15 September 2000. Revised 26 October 2001.


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