A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 5, p. 1433-1464

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.

DOI : https://doi.org/10.1051/m2an/2013076
Classification:  35Q35,  65M12,  65M60
Keywords: liquid crystal, Navier-Stokes, stability, convergence, finite elements, penalization
@article{M2AN_2013__47_5_1433_0,
author = {Guill\'en-Gonz\'alez, F. M. and Guti\'errez-Santacreu, J. V.},
title = {A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {47},
number = {5},
year = {2013},
pages = {1433-1464},
doi = {10.1051/m2an/2013076},
zbl = {1290.82031},
mrnumber = {3100770},
language = {en},
url = {http://www.numdam.org/item/M2AN_2013__47_5_1433_0}
}

Guillén-González, F. M.; Gutiérrez-Santacreu, J. V. A linear mixed finite element scheme for a nematic Ericksen-Leslie liquid crystal model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 5, pp. 1433-1464. doi : 10.1051/m2an/2013076. http://www.numdam.org/item/M2AN_2013__47_5_1433_0/

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