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

F. M. Guillén-González; J. V. Gutiérrez-Santacreu

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2013)

  • Volume: 47, Issue: 5, page 1433-1464
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Guillén-González, F. M., and 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 47.5 (2013): 1433-1464. <http://eudml.org/doc/273341>.

@article{Guillén2013,
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.},
author = {Guillén-González, F. M., Gutiérrez-Santacreu, J. V.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {liquid crystal; Navier–Stokes; stability; convergence; finite elements; penalization; Ericksen-Leslie system; Navier-Stokes equation; computational method; finite element scheme},
language = {eng},
number = {5},
pages = {1433-1464},
publisher = {EDP-Sciences},
title = {A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model},
url = {http://eudml.org/doc/273341},
volume = {47},
year = {2013},
}

TY - JOUR
AU - Guillén-González, F. M.
AU - Gutiérrez-Santacreu, J. V.
TI - A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2013
PB - EDP-Sciences
VL - 47
IS - 5
SP - 1433
EP - 1464
AB - 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.
LA - eng
KW - liquid crystal; Navier–Stokes; stability; convergence; finite elements; penalization; Ericksen-Leslie system; Navier-Stokes equation; computational method; finite element scheme
UR - http://eudml.org/doc/273341
ER -

References

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