A dual singular complement method for the numerical solution of the Poisson equation with $L^2$ boundary data in non-convex domains
Numerical Analysis
2015-05-12 v2
Abstract
The very weak solution of the Poisson equation with boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges with order in convex domains but has a reduced convergence order in non-convex domains. As a remedy, a dual variant of the singular complement method is proposed. The error order of the convex case is retained. Numerical experiments confirm the theoretical results.
Keywords
Cite
@article{arxiv.1505.00414,
title = {A dual singular complement method for the numerical solution of the Poisson equation with $L^2$ boundary data in non-convex domains},
author = {Thomas Apel and Serge Nicaise and Johannes Pfefferer},
journal= {arXiv preprint arXiv:1505.00414},
year = {2015}
}