A posteriori error estimates with point sources in fractional Sobolev spaces
Numerical Analysis
2015-07-30 v1
Abstract
We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a posteriori estimators with a specifically tailored oscillation and show that, on two-dimensional polygonal domains, they are reliable and locally efficient. In numerical tests, their use in an adaptive algorithm leads to optimal error decay rates.
Keywords
Cite
@article{arxiv.1507.08247,
title = {A posteriori error estimates with point sources in fractional Sobolev spaces},
author = {Fernando D. Gaspoz and Pedro Morin and Andreas Veeser},
journal= {arXiv preprint arXiv:1507.08247},
year = {2015}
}