Mixed methods for the approximation of liquid crystal flows

Chun Liu; Noel J. Walkington

doi:10.1051/m2an:2002010

Mixed methods for the approximation of liquid crystal flows

Chun Liu
, Noel J. Walkington

Research output: Contribution to journal › Article › peer-review

57 Scopus citations

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.

Original language	English (US)
Pages (from-to)	205-222
Number of pages	18
Journal	Mathematical Modelling and Numerical Analysis
Volume	36
Issue number	2
DOIs	https://doi.org/10.1051/m2an:2002010
State	Published - 2002

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Modeling and Simulation
Computational Mathematics
Applied Mathematics

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10.1051/m2an:2002010

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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.",

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T1 - Mixed methods for the approximation of liquid crystal flows

AU - Liu, Chun

AU - Walkington, Noel J.

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N2 - 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.

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.

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UR - https://www.scopus.com/pages/publications/0035999311#tab=citedBy

U2 - 10.1051/m2an:2002010

DO - 10.1051/m2an:2002010

M3 - Article

AN - SCOPUS:0035999311

SN - 0764-583X

VL - 36

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EP - 222

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 2

ER -

Mixed methods for the approximation of liquid crystal flows

Abstract

All Science Journal Classification (ASJC) codes

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