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dc.creatorBadia Rodríguez, Santiagoes
dc.creatorGuillén González, Francisco Manueles
dc.creatorGutiérrez Santacreu, Juan Vicentees
dc.date.accessioned2016-10-21T06:20:10Z
dc.date.available2016-10-21T06:20:10Z
dc.date.issued2011-09
dc.identifier.citationBadia Rodríguez, S., Guillén González, F.M. y Gutiérrez Santacreu, J.V. (2011). An overview on numerical analyses of nematic liquid crystal flows. Archives of Computational Methods in Engineering, 18, 285-313.
dc.identifier.issn1134-3060es
dc.identifier.issn1886-1784es
dc.identifier.urihttp://hdl.handle.net/11441/47880
dc.description.abstractThe purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid crystals. The Ericksen-Leslie equations govern the motion of a nematic liquid crystal. This system, in its simplest form, consists of the Navier-Stokes equations coupled with an extra anisotropic stress tensor, which represents the effect of the nematic liquid crystal on the fluid, and a convective harmonic map equation. The sphere constraint must be enforced almost everywhere in order to obtain an energy estimate. Since an almost everywhere satisfaction of this restriction is not appropriate at a numerical level, two alternative approaches have been introduced: a penalty method and a saddle-point method. These approaches are suitable for their numerical approximation by finite elements, since a discrete version of the restriction is enough to prove the desired energy estimate. The Ginzburg-Landau penalty function is usually used to enforce the sphere constraint. Finite element methods of mixed type will play an important role when designing numerical approximations for the penalty method in order to preserve the intrinsic energy estimate. The inf-sup condition that makes the saddle-point method well-posed is not clear yet. The only inf-sup condition for the Lagrange multiplier is obtained in the dual space of H1(Ω). But such an inf-sup condition requires more regularity for the director vector than the one provided by the energy estimate. Herein, we will present an alternative inf-sup condition whose proof for its discrete counterpart with finite elements is still open.es
dc.description.sponsorshipMinisterio de Ciencia e Innovaciónes
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherSpringeres
dc.relation.ispartofArchives of Computational Methods in Engineering, 18, 285-313.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.titleAn overview on numerical analyses of nematic liquid crystal flowses
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/submittedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numéricoes
dc.relation.projectIDMTM2009-12927es
dc.relation.publisherversionhttp://download.springer.com/static/pdf/131/art%253A10.1007%252Fs11831-011-9061-x.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs11831-011-9061-x&token2=exp=1477031872~acl=%2Fstatic%2Fpdf%2F131%2Fart%25253A10.1007%25252Fs11831-011-9061-x.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs11831-011-9061-x*~hmac=d00eb94c935a3c8eded907da0a7dff96caf1a08e0f311a1edac5fceaed2ca944es
dc.identifier.doi10.1007/s11831-011-9061-xes
dc.contributor.groupUniversidad de Sevilla. FQM131: Ec.diferenciales,Simulación Num.y Desarrollo Softwarees
idus.format.extent54 p.es
dc.journaltitleArchives of Computational Methods in Engineeringes
dc.publication.volumen18es
dc.publication.initialPage285es
dc.publication.endPage313es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/47880
dc.contributor.funderMinisterio de Ciencia e Innovación (MICIN). España

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