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
Original languageEnglish
Place of PublicationGlasgow
PublisherUniversity of Strathclyde
Number of pages17
Volume2011-16
Publication statusPublished - 2011

Keywords

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

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