Robust coupling of DPG and BEM for a singularly perturbed transmission problem (Q1668558)

A transmission problem is considered. Precisely, a singularly perturbed reaction diffusion equation is given on a bounded domain and the Laplacian is given in the exterior domain. Both domains are coupled by standard transmission conditions. The authors establish a DPG (discontinuous Petrov-Galerkin method with optimal test functions) which is coupled with a BEM (Galerkin boundary element method). Further, they show the robustness for the field variables in the so-called balanced norms. Their coupling scheme depends on the one given in the paper [Math. Comput. 86, No. 307, 2261--2284 (2017; Zbl 1364.65248)] by \textit{T. Führer} et al. and is adapted to the singularly perturbed case by using the scheme of \textit{N. Heuer} and \textit{M. Karkulik} [``DPG method with optimal test functions for a transmission problem'', Comput. Math. Appl. 70, No. 5, 1504--1518 (2015; \url{doi:10.1016/j.camwa.2015.06.032})]. It is shown that the optimal test functions in the new method have to be computed only locally. Various numerical experiments in two dimensions are given to support the theory.