A robust DPG method for large domains
Numerical Analysis
2020-11-25 v1 Numerical Analysis
Abstract
We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincar\'e-type inequality. We show how robustness can be re-established by using appropriately scaled test norms. As model cases we study the Poisson problem and the Kirchhoff--Love plate bending model, and also include fully discrete variants where optimal test functions are approximated. Numerical experiments for both model problems, including an-isotropic domains and mixed boundary conditions, confirm our findings.
Cite
@article{arxiv.2011.12098,
title = {A robust DPG method for large domains},
author = {Thomas Führer and Norbert Heuer},
journal= {arXiv preprint arXiv:2011.12098},
year = {2020}
}