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

 

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Opened Access A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model
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Author: Guillén González, Francisco Manuel
Gutiérrez Santacreu, Juan Vicente
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2013-09
Published in: ESAIM : Mathematical modelling and numerical analysis
Document type: Article
Abstract: 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.
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URI: http://hdl.handle.net/11441/41259

DOI: http://dx.doi.org/10.1051/m2an/2013076

This work is under a Creative Commons License: 
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