Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem

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Maity, Ruma Rani and Majumdar, Apala and Nataraj, Neela (2020) Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem. Computational Methods in Applied Mathematics, 21 (1). 179–209. ISSN 1609-9389 (https://doi.org/10.1515/cmam-2020-0185)

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Abstract

We study a system of semi-linear elliptic partial differential equations with a lower order cubic nonlinear term, and inhomogeneous Dirichlet boundary conditions, relevant for two-dimensional bistable liquid crystal devices, within a reduced Landau–de Gennes framework. The main results are (i) a priori error estimates for the energy norm, within the Nitsche’s and discontinuous Galerkin frameworks under milder regularity assumptions on the exact solution and (ii) a reliable and efficient a posteriori analysis for a sufficiently large penalization parameter and a sufficiently fine triangulation in both cases. Numerical examples that validate the theoretical results, are presented separately.

ORCID iDs

Maity, Ruma Rani, Majumdar, Apala ORCID logoORCID: https://orcid.org/0000-0003-4802-6720 and Nataraj, Neela;
  • Item type:Article
    ID code:74999
    Dates:
    Date
    Event
    16 December 2020
    Published
    16 December 2020
    Published Online
    3 December 2020
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:07 Jan 2021 15:56
    Last modified:11 Nov 2024 12:56
    URI:https://strathprints.strath.ac.uk/id/eprint/74999
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