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

Craig MacDonald, John MacKenzie, Alison Ramage, Chris Newton

Research output: Working paper

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 soluction converges at an otimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter
LanguageEnglish
Place of PublicationGlasgow
PublisherUniversity of Strathclyde
Number of pages17
Volume2011-16
Publication statusPublished - 2011

Fingerprint

Nematic Liquid Crystal
Monitor
Tensor
Non-uniform Mesh
Adaptive Finite Element Method
Singularly Perturbed Boundary Value Problem
Adaptive Mesh
Equidistribution
Nonlinear Boundary Value Problems
Strictly positive
Singular Perturbation
Liquid Crystal
Linear Combination
Numerical Solution
Mesh
Converge
Derivative
Model

Keywords

  • robust
  • adaptive computation
  • one-dimensional
  • q-tensor model
  • nematic liquid crystals
  • uniform convergence
  • adaptive grids
  • mesh equidistribution
  • monitor function

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 soluction converges at an otimal 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.

Glasgow : University of Strathclyde, 2011.

Research output: Working paper

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T1 - Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals

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AU - MacKenzie, John

AU - Ramage, Alison

AU - Newton, Chris

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N2 - 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 soluction converges at an otimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter

AB - 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 soluction converges at an otimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter

KW - robust

KW - adaptive computation

KW - one-dimensional

KW - q-tensor model

KW - nematic liquid crystals

KW - uniform convergence

KW - adaptive grids

KW - mesh equidistribution

KW - monitor function

UR - http://www.mathstat.strath.ac.uk/research/reports/2011

M3 - Working paper

VL - 2011-16

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

PB - University of Strathclyde

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