Mixed methods for the approximation of liquid crystal flows

Chun Liu; Noel J. Walkington

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 2, page 205-222
  • ISSN: 0764-583X

Abstract

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The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve H 2 ( Ω ) norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.

How to cite

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Liu, Chun, and Walkington, Noel J.. "Mixed methods for the approximation of liquid crystal flows." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.2 (2002): 205-222. <http://eudml.org/doc/245086>.

@article{Liu2002,
abstract = {The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve $\{H^2(\Omega )\}$ norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.},
author = {Liu, Chun, Walkington, Noel J.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {liquid crystals; mixed finite element approximation; convergence; Ericksen-Leslie equations; energy estimates; director field},
language = {eng},
number = {2},
pages = {205-222},
publisher = {EDP-Sciences},
title = {Mixed methods for the approximation of liquid crystal flows},
url = {http://eudml.org/doc/245086},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Liu, Chun
AU - Walkington, Noel J.
TI - Mixed methods for the approximation of liquid crystal flows
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 2
SP - 205
EP - 222
AB - The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve ${H^2(\Omega )}$ norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.
LA - eng
KW - liquid crystals; mixed finite element approximation; convergence; Ericksen-Leslie equations; energy estimates; director field
UR - http://eudml.org/doc/245086
ER -

References

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