Robust coupling of DPG and BEM for a singularly perturbed transmission   problem
  We consider a transmission problem consisting of a singularly perturbed reaction diffusion equation on a bounded domain and the Laplacian in the exterior, connected through standard transmission conditions. We establish a DPG scheme coupled with Galerkin boundary elements for its discretization, and prove its robustness for the field variables in so-called balanced norms. Our coupling scheme is the one from [F\"uhrer, Heuer, Karkulik: On the coupling of DPG and BEM, arXiv:1508.00630], adapted to the singularly perturbed case by using the scheme from [Heuer, Karkulik: A robust DPG method for singularly perturbed reaction diffusion problems, arXiv:1509.07560]. Essential feature of our method is that optimal test functions have to be computed only locally. We report on various numerical experiments in two dimensions. 
Thomas F\"uhrer and Norbert Heuer
math.NA