Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals

Craig MacDonald, John MacKenzie, Alison Ramage, Chris Newton

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper illustrates the use of an adaptive finite element method to solve a non-linear singularly perturbed boundary value problem which arises from a one-dimensional q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a strictly positive monitor function which is a linear combination of a constant floor and a power of the first derivative of the numerical solution. by an appropriate selection of the monitor function parameters, we show that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter.
LanguageEnglish
Pages3627-3640
Number of pages14
JournalComputers and Mathematics with Applications
Volume64
Issue number11
DOIs
Publication statusPublished - Dec 2012

Fingerprint

Nematic liquid crystals
Nematic Liquid Crystal
Tensors
Monitor
Tensor
Numerical Solution
Non-uniform Mesh
Adaptive Finite Element Method
Singularly Perturbed Boundary Value Problem
Adaptive Mesh
Equidistribution
Optimal Rates
Nonlinear Boundary Value Problems
Strictly positive
Singular Perturbation
Liquid Crystal
Liquid crystals
Boundary value problems
Linear Combination
Mesh

Keywords

  • liquid crystals
  • adaptive computation
  • q-tensor model

Cite this

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abstract = "This paper illustrates the use of an adaptive finite element method to solve a non-linear singularly perturbed boundary value problem which arises from a one-dimensional q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a strictly positive monitor function which is a linear combination of a constant floor and a power of the first derivative of the numerical solution. by an appropriate selection of the monitor function parameters, we show that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter.",
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Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals. / MacDonald, Craig; MacKenzie, John; Ramage, Alison; Newton, Chris.

In: Computers and Mathematics with Applications, Vol. 64, No. 11, 12.2012, p. 3627-3640.

Research output: Contribution to journalArticle

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