DPG method with optimal test functions for a transmission problem
Numerical Analysis
2014-12-16 v1
Abstract
We propose and analyze a numerical method to solve an elliptic transmission problem in full space. The method consists of a variational formulation involving standard boundary integral operators on the coupling interface and an ultra-weak formulation in the interior. To guarantee the discrete inf-sup condition, the system is discretized by the DPG method with optimal test functions. We prove that principal unknowns are approximated quasi-optimally. Numerical experiments for problems with smooth and singular solutions confirm optimal convergence orders.
Cite
@article{arxiv.1412.4753,
title = {DPG method with optimal test functions for a transmission problem},
author = {Norbert Heuer and Michael Karkulik},
journal= {arXiv preprint arXiv:1412.4753},
year = {2014}
}