Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm

Handle URI:
http://hdl.handle.net/10754/564820
Title:
Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm
Authors:
Niemi, Antti H.; Collier, Nathaniel Oren; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. © 2013 Elsevier Ltd. All rights reserved.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program
Publisher:
Elsevier BV
Journal:
Computers & Mathematics with Applications
Conference/Event name:
ICNC-FSKD 2012
Issue Date:
Dec-2013
DOI:
10.1016/j.camwa.2013.07.016
ARXIV:
arXiv:1201.1847
Type:
Conference Paper
ISSN:
08981221
Additional Links:
http://arxiv.org/abs/arXiv:1201.1847v1
Appears in Collections:
Conference Papers; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorNiemi, Antti H.en
dc.contributor.authorCollier, Nathaniel Orenen
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-08-04T07:17:11Zen
dc.date.available2015-08-04T07:17:11Zen
dc.date.issued2013-12en
dc.identifier.issn08981221en
dc.identifier.doi10.1016/j.camwa.2013.07.016en
dc.identifier.urihttp://hdl.handle.net/10754/564820en
dc.description.abstractWe investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. © 2013 Elsevier Ltd. All rights reserved.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1201.1847v1en
dc.subjectAutomatic stabilization techniqueen
dc.subjectConvection-dominated diffusionen
dc.subjectDiscontinuous Petrov-Galerkinen
dc.subjectFinite element methoden
dc.subjectNumerical stabilityen
dc.subjectRobustnessen
dc.titleAutomatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space normen
dc.typeConference Paperen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.identifier.journalComputers & Mathematics with Applicationsen
dc.conference.nameICNC-FSKD 2012en
dc.contributor.institutionAalto University, School of Engineering, Department of Civil and Structural Engineering, Espoo, Finlanden
dc.identifier.arxividarXiv:1201.1847en
kaust.authorCollier, Nathaniel Orenen
kaust.authorCalo, Victor M.en
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