Mixed Methods for the Approximation of Liquid Crystal Flows

Chun Liu; Noel J. Walkington

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 H2(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 36.2 (2010): 205-222. <http://eudml.org/doc/194101>.

@article{Liu2010,
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 H2(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. },
author = {Liu, Chun, Walkington, Noel J.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Liquid Crystals; Mixed Finite Element Approximation; Convergence.; Ericksen-Leslie equations; mixed finite element approximation; convergence; energy estimates; director field},
language = {eng},
month = {3},
number = {2},
pages = {205-222},
publisher = {EDP Sciences},
title = {Mixed Methods for the Approximation of Liquid Crystal Flows},
url = {http://eudml.org/doc/194101},
volume = {36},
year = {2010},
}

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
DA - 2010/3//
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 H2(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.
LA - eng
KW - Liquid Crystals; Mixed Finite Element Approximation; Convergence.; Ericksen-Leslie equations; mixed finite element approximation; convergence; energy estimates; director field
UR - http://eudml.org/doc/194101
ER -

References

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