Ultra-weak formulation of a hypersingular integral equation on polygons and DPG method with optimal test functions
Numerical Analysis
2013-09-09 v1
Abstract
We present an ultra-weak formulation of a hypersingular integral equation on closed polygons and prove its well-posedness and equivalence with the standard variational formulation. Based on this ultra-weak formulation we present a discontinuous Petrov-Galerkin method with optimal test functions and prove its quasi-optimal convergence in . Theoretical results are confirmed by numerical experiments on an open curve with uniform and adaptively refined meshes.
Keywords
Cite
@article{arxiv.1309.1697,
title = {Ultra-weak formulation of a hypersingular integral equation on polygons and DPG method with optimal test functions},
author = {Norbert Heuer and Felipe Pinochet},
journal= {arXiv preprint arXiv:1309.1697},
year = {2013}
}
Comments
23 pages, 2 figures