Runge-Kutta approximation for $C_0$-semigroups in the graph norm with applications to time domain boundary integral equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866916334340669440 |
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| author | Rieder, Alexander Sayas, Francisco-Javier Melenk, Jens Markus |
| author_facet | Rieder, Alexander Sayas, Francisco-Javier Melenk, Jens Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_01996 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Runge-Kutta approximation for $C_0$-semigroups in the graph norm with applications to time domain boundary integral equations Rieder, Alexander Sayas, Francisco-Javier Melenk, Jens Markus Numerical Analysis 65N38, 65N12, 80M15 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. |
| title | Runge-Kutta approximation for $C_0$-semigroups in the graph norm with applications to time domain boundary integral equations |
| topic | Numerical Analysis 65N38, 65N12, 80M15 |
| url | https://arxiv.org/abs/2003.01996 |