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

Authors:
Craig S. Macdonald;John A. Mackenzie;Alison Ramage;Christopher J. P. Newton
Affiliations:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, Scotland, United Kingdom;Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, Scotland, United Kingdom;Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, Scotland, United Kingdom;Hewlett-Packard Laboratories, Long Down Avenue, Stoke Gifford, Bristol BS34 8QZ, England, United Kingdom
Venue:
Computers & Mathematics with Applications
Year:
2012

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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 the singular perturbation parameter.