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Adaptive solution of a one-dimensional order reconstruction problem in Q-tensor theory of liquid crystals

Ramage, A. and Newton, C.J.P. (2007) Adaptive solution of a one-dimensional order reconstruction problem in Q-tensor theory of liquid crystals. Liquid Crystals, 34 (4). pp. 479-487. ISSN 0267-8292

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In this paper we illustrate the suitability of an adaptive moving mesh method for modelling a one-dimensional liquid crystal cell using Q-tensor theory. Specifically, we consider a time-dependent problem in a Pi-cell geometry which admits two topologically different equilibrium states and model the order reconstruction which occurs on the application of an electric field. An adaptive finite element grid is used where the grid points are moved according to equidistribution of a monitor function based on a specific property of the Q-tensor. We show that such moving meshes provide the same level of accuracy as uniform grids but using far fewer points, and that inaccurate results can be obtained if uniform grids are not sufficiently refined.