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

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MacDonald, Craig and MacKenzie, John and Ramage, Alison and Newton, Chris (2012) Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals. Computers and Mathematics with Applications, 64 (11). pp. 3627-3640. ISSN 0898-1221 (https://doi.org/10.1016/j.camwa.2012.10.003)

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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 singular perturbation parameter.

ORCID iDs

MacDonald, Craig ORCID logoORCID: https://orcid.org/0000-0002-9996-674X, MacKenzie, John ORCID logoORCID: https://orcid.org/0000-0003-4412-7057, Ramage, Alison ORCID logoORCID: https://orcid.org/0000-0003-4709-0691 and Newton, Chris;
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