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dc.contributor.authorMuñoz-Matute, J. 
dc.contributor.authorPardo, D. 
dc.contributor.authorCalo, V.M.
dc.contributor.authorAlberdi, E.
dc.date.accessioned2019-09-08T20:25:15Z
dc.date.available2019-09-08T20:25:15Z
dc.date.issued2019-08
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1008
dc.description.abstractVariational 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.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectlinear diffusion equationen_US
dc.subjectdiscontinuous Petrov-Galerkin formulationsen_US
dc.subjectdynamic meshesen_US
dc.subjectRunge-Kutta methodsen_US
dc.titleVariational Formulations for Explicit Runge-Kutta Methodsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.arxivarXiv:1806.07803
dc.identifier.doihttps://doi.org/10.1016/j.finel.2019.06.007
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0168874X18308230en_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/777778en_US
dc.relation.projectIDES/1PE/MTM2016-76329-Ren_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleFinite Elements in Analysis and Designen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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