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

4 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.
Original languageEnglish
Pages (from-to)3627-3640
Number of pages14
JournalComputers and Mathematics with Applications
Volume64
Issue number11
DOIs
Publication statusPublished - Dec 2012

Keywords

  • liquid crystals
  • adaptive computation
  • q-tensor model

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