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

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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.

ORCID iDs

Nochetto, Ricardo H., Ruggeri, Michele ORCID logoORCID: https://orcid.org/0000-0001-6213-1602 and Yang, Shuo;
  • 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 Nov 2024 13:28
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/80266
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