Local inverse estimates for non-local boundary integral operators
Numerical Analysis
2017-12-04 v1
Abstract
We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded d-dimensional Lipschitz domain Omega for d >= 2 with piecewise smooth boundary. For piecewise polynomial ansatz spaces and d = 2 or 3, the inverse estimates are explicit in both the local mesh width and the approximation order. An application to efficiency estimates in a posteriori error estimation in boundary element methods is given.
Cite
@article{arxiv.1504.04394,
title = {Local inverse estimates for non-local boundary integral operators},
author = {Markus Aurada and Michael Feischl and Thomas Führer and Michael Karkulik and Jens Markus Melenk and Dirk Praetorius},
journal= {arXiv preprint arXiv:1504.04394},
year = {2017}
}