Variational Formulations for Explicit Runge-Kutta Methods

Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known that implicit time marching schemes have variational structure, they are often employ...

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Detalles Bibliográficos
Autores: Muñoz-Matute, J., Pardo, D., Calo, V.M., Alberdi, E.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1008
Acceso en línea:http://hdl.handle.net/20.500.11824/1008
https://doi.org/10.1016/j.finel.2019.06.007
Access Level:acceso abierto
Palabra clave:linear diffusion equation
discontinuous Petrov-Galerkin formulations
dynamic meshes
Runge-Kutta methods
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spelling Variational Formulations for Explicit Runge-Kutta MethodsMuñoz-Matute, J.Pardo, D.Calo, V.M.Alberdi, E.linear diffusion equationdiscontinuous Petrov-Galerkin formulationsdynamic meshesRunge-Kutta methodsVariational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known that implicit time marching schemes have variational structure, they are often employed for adaptivity. Previously, Galerkin formulations of explicit methods were introduced for ordinary di fferential equations employing speci fic inexact quadrature rules. In this work, we prove that the explicit Runge-Kutta methods can be expressed as discontinuous-in-time Petrov-Galerkin methods for the linear di ffusion equation. We systematically build trial and test functions that, after exact integration in time, lead to one, two, and general stage explicit Runge-Kutta methods. This approach enables us to reproduce the existing time-domain (goal-oriented) adaptive algorithms using explicit methods in time.201920192019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1008https://doi.org/10.1016/j.finel.2019.06.007reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/pii/S0168874X18308230info:eu-repo/grantAgreement/EC/H2020/777778info:eu-repo/grantAgreement/MINECO//MTM2016-76329-RReconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/10082026-06-19T12:47:47Z
dc.title.none.fl_str_mv Variational Formulations for Explicit Runge-Kutta Methods
title Variational Formulations for Explicit Runge-Kutta Methods
spellingShingle Variational Formulations for Explicit Runge-Kutta Methods
Muñoz-Matute, J.
linear diffusion equation
discontinuous Petrov-Galerkin formulations
dynamic meshes
Runge-Kutta methods
title_short Variational Formulations for Explicit Runge-Kutta Methods
title_full Variational Formulations for Explicit Runge-Kutta Methods
title_fullStr Variational Formulations for Explicit Runge-Kutta Methods
title_full_unstemmed Variational Formulations for Explicit Runge-Kutta Methods
title_sort Variational Formulations for Explicit Runge-Kutta Methods
dc.creator.none.fl_str_mv Muñoz-Matute, J.
Pardo, D.
Calo, V.M.
Alberdi, E.
author Muñoz-Matute, J.
author_facet Muñoz-Matute, J.
Pardo, D.
Calo, V.M.
Alberdi, E.
author_role author
author2 Pardo, D.
Calo, V.M.
Alberdi, E.
author2_role author
author
author
dc.subject.none.fl_str_mv linear diffusion equation
discontinuous Petrov-Galerkin formulations
dynamic meshes
Runge-Kutta methods
topic linear diffusion equation
discontinuous Petrov-Galerkin formulations
dynamic meshes
Runge-Kutta methods
description Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known that implicit time marching schemes have variational structure, they are often employed for adaptivity. Previously, Galerkin formulations of explicit methods were introduced for ordinary di fferential equations employing speci fic inexact quadrature rules. In this work, we prove that the explicit Runge-Kutta methods can be expressed as discontinuous-in-time Petrov-Galerkin methods for the linear di ffusion equation. We systematically build trial and test functions that, after exact integration in time, lead to one, two, and general stage explicit Runge-Kutta methods. This approach enables us to reproduce the existing time-domain (goal-oriented) adaptive algorithms using explicit methods in time.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019
2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1008
https://doi.org/10.1016/j.finel.2019.06.007
url http://hdl.handle.net/20.500.11824/1008
https://doi.org/10.1016/j.finel.2019.06.007
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/pii/S0168874X18308230
info:eu-repo/grantAgreement/EC/H2020/777778
info:eu-repo/grantAgreement/MINECO//MTM2016-76329-R
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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