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dc.contributor.authorBadia, Santiago
dc.contributor.authorCodina, Ramon
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Resistència de Materials i Estructures a l'Enginyeria
dc.date.accessioned2012-04-18T17:27:57Z
dc.date.available2012-04-18T17:27:57Z
dc.date.created2012-04
dc.date.issued2012-04
dc.identifier.citationS. Badia; Codina, R. Stokes, Maxwell and Darcy: a single finite element approximation for three model problems. "Applied numerical mathematics", Abril 2012, vol. 62, núm. 4, p. 246-263.
dc.identifier.issn0168-9274
dc.identifier.urihttp://hdl.handle.net/2117/15742
dc.description.abstractIn this work we propose stabilized finite element methods for Stokes’, Maxwell’s and Darcy’s problems that accommodate any interpolation of velocities and pressures. We briefly review the formulations we have proposed for these three problems independently in a unified manner, stressing the advantages of our approach. In particular, for Darcy’s problem we are able to design stabilized methods that yield optimal convergence both for the primal and the dual problems. In the case of Maxwell’s problem, the formulation we propose allows one to use continuous finite element interpolations that converge optimally to the continuous solution even if it is non-smooth. Once the formulation is presented for the three model problems independently, we also show how it can be used for a problem that combines all the operators of the independent problems. Stability and convergence is achieved regardless of the fact that any of these operators dominates the others, a feature not possible for the methods of which we are aware.
dc.format.extent18 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
dc.subject.lcshNavier-Stokes equations--Numerical solutions
dc.subject.lcshMaxwell equations--Numerical solutions
dc.subject.lcshDarcy's law
dc.subject.otherStabilized finiteelements
dc.subject.otherCompatible approximations
dc.subject.otherPrimal and dual problems
dc.subject.otherSingular solutions
dc.subject.otherNodal interpolations
dc.titleStokes, Maxwell and Darcy: a single finite element approximation for three model problems
dc.typeArticle
dc.subject.lemacEquacions de Navier-Stokes
dc.subject.lemacMaxwell, Equacions de -- Solucions numèriques
dc.contributor.groupUniversitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus
dc.identifier.doi10.1016/j.apnum.2011.07.001
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0168927411001097
dc.rights.accessOpen Access
local.identifier.drac10254494
dc.description.versionPreprint
local.citation.authorS. Badia; Codina, R.
local.citation.publicationNameApplied numerical mathematics
local.citation.volume62
local.citation.number4
local.citation.startingPage246
local.citation.endingPage263


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