Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems

Abstract

In this paper we apply the coupling of mixed finite element and boundary integral methods for solving some class of linear and nonlinear elliptic boundary value problems. As a model case we consider the two-domensional Laplacian coupled with a second order elliptic equation in divergence frorm which may also be nonlinear. Such problems arise, e.g., in nonlinear magnetic field computations. Our analysis is based on Brezzi's theory for linear constrained variational problems, and on some nonlinear functional analysis. We show existence and uniqueness for the continuous variational formulations, and derive general approximation results for the corresponding Galerkin achemes.