A weighted setting for the numerical approximation of the Poisson problem with singular sources
Numerical Analysis
2018-09-12 v1
Abstract
We consider the approximation of Poisson type problems where the source is given by a singular measure and the domain is a convex polygonal or polyhedral domain. First, we prove the well-posedness of the Poisson problem when the source belongs to the dual of a weighted Sobolev space where the weight belongs to the Muckenhoupt class. Second, we prove the stability in weighted norms for standard finite element approximations under the quasi-uniformity assumption on the family of meshes.
Cite
@article{arxiv.1809.03529,
title = {A weighted setting for the numerical approximation of the Poisson problem with singular sources},
author = {Irene Drelichman and Ricardo Durán and Ignacio Ojea},
journal= {arXiv preprint arXiv:1809.03529},
year = {2018}
}
Comments
13 pages