Discontinuous Petrov-Galerkin method based on the optimal test space norm for steady transport problems in one space dimension

Handle URI:
http://hdl.handle.net/10754/562741
Title:
Discontinuous Petrov-Galerkin method based on the optimal test space norm for steady transport problems in one space dimension
Authors:
Niemi, Antti; Collier, Nathaniel Oren; Calo, Victor M. ( 0000-0002-1805-4045 )
Abstract:
We revisit the finite element analysis of convection-dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the optimal test space norm. This makes the DPG method not only stable but also robust, that is, uniformly stable with respect to the Péclet number in the current application. We employ discontinuous piecewise Bernstein polynomials as trial functions and construct a subgrid discretization that accounts for the singular perturbation character of the problem to resolve the corresponding optimal test functions. We also show that a smooth B-spline basis has certain computational advantages in the subgrid discretization. The overall effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation. © 2011 Elsevier B.V.
KAUST Department:
Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Numerical Porous Media SRI Center (NumPor)
Publisher:
Elsevier
Journal:
Journal of Computational Science
Issue Date:
May-2013
DOI:
10.1016/j.jocs.2011.07.003
Type:
Article
ISSN:
18777503
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorNiemi, Anttien
dc.contributor.authorCollier, Nathaniel Orenen
dc.contributor.authorCalo, Victor M.en
dc.date.accessioned2015-08-03T11:03:59Zen
dc.date.available2015-08-03T11:03:59Zen
dc.date.issued2013-05en
dc.identifier.issn18777503en
dc.identifier.doi10.1016/j.jocs.2011.07.003en
dc.identifier.urihttp://hdl.handle.net/10754/562741en
dc.description.abstractWe revisit the finite element analysis of convection-dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the optimal test space norm. This makes the DPG method not only stable but also robust, that is, uniformly stable with respect to the Péclet number in the current application. We employ discontinuous piecewise Bernstein polynomials as trial functions and construct a subgrid discretization that accounts for the singular perturbation character of the problem to resolve the corresponding optimal test functions. We also show that a smooth B-spline basis has certain computational advantages in the subgrid discretization. The overall effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation. © 2011 Elsevier B.V.en
dc.publisherElsevieren
dc.subjectConvection-diffusionen
dc.subjectDiscontinuous Petrov-Galerkinen
dc.subjectFinite element methoden
dc.subjectUnconditional stabilityen
dc.titleDiscontinuous Petrov-Galerkin method based on the optimal test space norm for steady transport problems in one space dimensionen
dc.typeArticleen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalJournal of Computational Scienceen
kaust.authorNiemi, Anttien
kaust.authorCollier, Nathaniel Orenen
kaust.authorCalo, Victor M.en
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