On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates
Numerical Analysis
2024-02-14 v1 Numerical Analysis
Abstract
In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependent partial differential equations. It turns out that the stability constant depends linearly on the finite element mesh parameter, but in most cases, we can show optimal convergence. We present a series of numerical experiments which illustrate the theoretical findings.
Cite
@article{arxiv.2402.08291,
title = {On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates},
author = {Richard Löscher and Olaf Steinbach and Marco Zank},
journal= {arXiv preprint arXiv:2402.08291},
year = {2024}
}