Robust coupling of DPG and BEM for a singularly perturbed transmission problem
Abstract
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.
Cite
@article{arxiv.1603.05164,
title = {Robust coupling of DPG and BEM for a singularly perturbed transmission problem},
author = {Thomas Führer and Norbert Heuer},
journal= {arXiv preprint arXiv:1603.05164},
year = {2016}
}
Comments
Update of numerical examples