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In this paper we propose and analyze some new methods for cou- pling mixed flnite element and boundary element methods for the model prob- lem of the Laplace equation in free space or in the exterior of a bounded domain. As opposed to the existing methods, which use the complete matrix of operators of the Calderon projector to obtain a symmetric coupled sys- tem, we propose methods with only one integral equation. The system can be considered as a further generalization of the Johnson{Nedelec coupling of BEM{FEM to the case of mixed formulations in the bounded domain. Using some recent analytical tools we are able to prove stability and convergence of Galerkin methods with very general conditions on the discrete spaces and no restriction relating the flnite and boundary element spaces. This can be done for general Lipschitz interfaces and in particular, the coupling boundary can be taken to be a Lipschitz polyhedron. Both the indirect and the direct approaches for the boundary integral formulation are explored. AMS Classiflcation. 65N30 Keywords. mixed FEM, BEM{FEM coupling, Lipschitz domains

Nonsymmetric coupling of BEM and mixed FEM on polyhedral interfaces