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

Abstract

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.

References in corpus (5)

• A fully discrete BEM-FEM scheme for transient acoustic waves
• A new and improved analysis of the time domain boundary integral operators for acoustics
• Runge-Kutta convolution quadrature and FEM-BEM coupling for the time dependent linear Schrödinger equation
• Time domain boundary integral equations and convolution quadrature for scattering by composite media (extended preprint)
• On superconvergence of Runge-Kutta convolution quadrature for the wave equation

Cited by in corpus (1)

• On superconvergence of Runge-Kutta convolution quadrature for the wave equation