Record link: 
http://hdl.handle.net/20.500.12708/137419
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Title: 
Runge-Kutta approximation for C₀-semigroups in the graph norm with applications to time domain boundary integral equations
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Citation: 
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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Publisher DOI: 
10.1007/s42985-020-00051-x
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Rieder, Alexander 
Sayas, Francisco-Javier 
Melenk, Jens Markus 
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Organisational Unit: 
E101-02 - Forschungsbereich Numerik 
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Journal: 
Partial Differential Equations and Applications 
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ISSN: 
2662-2963
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Date (published): 
2021
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Number of Pages: 
47
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Publisher: 
Springer Nature
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Peer reviewed: 
Yes
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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.
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Research Areas: 
Modelling and Simulation: 20%
Mathematical and Algorithmic Foundations: 80%
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Science Branch: 
Mathematik
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