Gamma-convergent projection-free finite element methods for nematic liquid crystals : the Ericksen model

Nochetto, Ricardo H. and Ruggeri, Michele and Yang, Shuo (2022) Gamma-convergent projection-free finite element methods for nematic liquid crystals : the Ericksen model. SIAM Journal on Numerical Analysis, 60 (2). pp. 856-887. ISSN 0036-1429 (https://doi.org/10.1137/21M1407495)

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Abstract

The Ericksen model for nematic liquid crystals couples a director field with a scalar degree of orientation variable and allows the formation of various defects with finite energy. We propose a simple but novel finite element approximation of the problem that can be implemented easily within standard finite element packages. Our scheme is projection-free and thus circumvents the use of weakly acute meshes, which are quite restrictive in three dimensions but are required by recent algorithms for convergence. We prove stability and $\Gamma$-convergence properties of the new method in the presence of defects. We also design an effective nested gradient flow algorithm for computing minimizers that controls the violation of the unit-length constraint of the director. We present several simulations in two and three dimensions that document the performance of the proposed scheme and its ability to capture quite intriguing defects.

  • Item type:Article
    ID code:80266
    Dates:
    Date
    Event
    30 April 2022
    Published
    19 April 2022
    Published Online
    12 November 2021
    Accepted
    30 March 2021
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:21 Apr 2022 15:46
    Last modified:11 Apr 2024 02:27
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/80266
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