Robust coupling of DPG and BEM for a singularly perturbed transmission problem
Thomas Führer and Norbert Heuer
Comput. Math. Appl. 74 (8), 1940-1954, 2017.
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
[Führer, Heuer, Karkulik:
On the coupling of DPG and BEM,
Math. Comp., 2017]
adapted to the singularly perturbed case by using the scheme from
[Heuer, Karkulik:
A robust DPG method for singularly perturbed reaction diffusion problems,
SIAM J. Numer. Anal., 2017].
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.