JournalszaaVol. 21, No. 3pp. 761–781

Solvability and Galerkin Approximations of a Class of Nonlinear Operator Equations

  • Gabriel N. Gatica

    Universidad de Concepción, Chile
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Abstract

We generalize the usual Babuska-Brezzi theory to a class of nonlinear variational problems with constraints. The corresponding operator equation has a dual-dual type structure since the nonlinear operator involved has itself a dual structure with a strongly monotone and Lipschitz-continuous main operator. We provide sufficient conditions for the existence and uniqueness of solution of the continuous and Galerkin formulations, and derive a Strang-type estimate for the associated error. An application to the coupling of mixed-FEM and BEM for a nonlinear transmission problem in potential theory is also described.

Cite this article

Gabriel N. Gatica, Solvability and Galerkin Approximations of a Class of Nonlinear Operator Equations. Z. Anal. Anwend. 21 (2002), no. 3, pp. 761–781

DOI 10.4171/ZAA/1107