We propose a general framework that allows for a new natural coupling of boundary element and a wide class of finite element methods (FEMs) for a model second-order elliptic problem. This class of FEMs includes mixed methods, discontinuous Galerkin methods and the continuous Galerkin method. We provide sufficient conditions guaranteeing the well-posedness of the methods and give several examples that include new as well as old methods.
Bibliographical noteFunding Information:
Supported in part by the National Science Foundation (grant DMS-0712955) and by the University of Minnesota Supercomputing Institute.
- boundary element methods
- discontinuous Galerkin methods