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

Published online by Cambridge University Press:  30 July 2013

F.M. Guillén-González  and
J.V. Gutiérrez-Santacreu
F.M. Guillén-González
Affiliation:
Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain.. guillen@us.es .
J.V. Gutiérrez-Santacreu
Affiliation:
Dpto. Matemática Aplicada I, University of Sevilla, Av. Reina Mercedes s/n, 41012 Sevilla, Spain.; juanvi@us.es .
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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.

Keywords

Liquid crystalNavier–Stokesstabilityconvergencefinite elementspenalization
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 5 , September 2013 , pp. 1433 - 1464
Copyright
© EDP Sciences, SMAI, 2013

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