We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with optimal test functions to (i) least-squares boundary elements and (ii) various variants of standard Galerkin boundary elements. An essential feature of our method is that, despite the use of boundary integral equations, optimal test functions have to be computed only locally. We apply our findings to a standard transmission problem in full space and present numerical experiments to validate our theory.
Führer, Thomas; Heuer, Norbert; and Karkulik, Michael, "On the Coupling of DPG and BEM" (2015). Mathematics and Statistics Faculty Publications and Presentations. 185.