Runge-Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations

Alexander Rieder; Francisco-Javier Sayas; Jens Markus Melenk

doi:10.1007/s42985-020-00051-x

Runge-Kutta approximation for $C_{0}$ -semigroups in the graph norm with applications to time domain boundary integral equations

SN Partial Differ Equ Appl. 2020;1(6):49. doi: 10.1007/s42985-020-00051-x. Epub 2020 Nov 24.

Authors

Alexander Rieder¹, Francisco-Javier Sayas², Jens Markus Melenk³

Affiliations

¹ Fakultät für Mathematik, Universität Wien, Vienna, Austria.
² Department of Mathematical Sciences, University of Delaware, Newark, DE USA.
³ Institut für Analysis und Scientific Computing, Technische Universität Wien, Vienna, Austria.

Abstract

We consider the approximation of an abstract evolution problem with inhomogeneous side constraint using A-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.