Runge-Kutta approximation for $C_0$-semigroups in the graph norm with applications to time domain boundary integral equations
Numerical Analysis
2024-07-25 v1 Numerical Analysis
Abstract
We consider the approximation to an abstract evolution problem with inhomogeneous side constraint using -stable Runge-Kutta methods. We derive a priori estimates in norms other than the underlying Banach space. Most notably, we derive estimates in the graph norm of the generator. These results are used to study convolution quadrature based discretizations of a wave scattering and a heat conduction problem.
Keywords
Cite
@article{arxiv.2003.01996,
title = {Runge-Kutta approximation for $C_0$-semigroups in the graph norm with applications to time domain boundary integral equations},
author = {Alexander Rieder and Francisco-Javier Sayas and Jens Markus Melenk},
journal= {arXiv preprint arXiv:2003.01996},
year = {2024}
}