A. Rieder, F. Sayas, J. Melenk:

"Runge-Kutta approximation for C_0-semigroups in the graph norm with applications to time domain boundary integral equations";

in: "ASC Report 6/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 37.

We consider the approximation to 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.

http://www.asc.tuwien.ac.at/preprint/2020/asc06x2020.pdf

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