A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model

In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit first-order integration in time, approximating an Ericksen–Leslie nematic liquid crystal model by means of a Ginzburg–Landau penalized problem. Conditional stability of this s...

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Detalhes bibliográficos
Autores: Guillén González, Francisco Manuel, Gutiérrez Santacreu, Juan Vicente
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41259
Acesso em linha:http://hdl.handle.net/11441/41259
https://doi.org/10.1051/m2an/2013076
Access Level:acceso abierto
Palavra-chave:Liquid crystal
Navier–Stokes
stability
convergence
finite elements
penalization
Descrição
Resumo:In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit first-order integration in time, approximating an Ericksen–Leslie nematic liquid crystal model by means of a Ginzburg–Landau penalized problem. Conditional stability of this scheme is proved via a discrete version of the energy law satisfied by the continuous problem, and conditional convergence towards generalized Young measure-valued solutions to the Ericksen–Leslie problem is showed when the discrete parameters (in time and space) and the penalty parameter go to zero at the same time. Finally, we will show some numerical experiences for a phenomenon of annihilation of singularities.