Rieder, A., Sayas, F.-J., & Melenk, J. M. (2021). Runge-Kutta approximation for C₀-semigroups in the graph norm with applications to time domain boundary integral equations. Partial Differential Equations and Applications, 1(6), Article 49. https://doi.org/10.1007/s42985-020-00051-x
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Journal:
Partial Differential Equations and Applications
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ISSN:
2662-2963
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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.
