Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations

We consider the approximation of 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...

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Detalles Bibliográficos
Autores principales: Rieder, Alexander, Sayas, Francisco-Javier, Melenk, Jens Markus
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7785590/
https://www.ncbi.nlm.nih.gov/pubmed/33458696
http://dx.doi.org/10.1007/s42985-020-00051-x
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author Rieder, Alexander
Sayas, Francisco-Javier
Melenk, Jens Markus
author_facet Rieder, Alexander
Sayas, Francisco-Javier
Melenk, Jens Markus
author_sort Rieder, Alexander
collection PubMed
description We consider the approximation of 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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spelling pubmed-77855902021-01-14 Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations Rieder, Alexander Sayas, Francisco-Javier Melenk, Jens Markus SN Partial Differ Equ Appl Original Paper We consider the approximation of 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. Springer International Publishing 2020-11-24 2020 /pmc/articles/PMC7785590/ /pubmed/33458696 http://dx.doi.org/10.1007/s42985-020-00051-x Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Original Paper
Rieder, Alexander
Sayas, Francisco-Javier
Melenk, Jens Markus
Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations
title Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations
title_full Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations
title_fullStr Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations
title_full_unstemmed Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations
title_short Runge–Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations
title_sort runge–kutta approximation for [formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7785590/
https://www.ncbi.nlm.nih.gov/pubmed/33458696
http://dx.doi.org/10.1007/s42985-020-00051-x
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