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

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

[thumbnail of Maity-etal-CMAM-2020-Error-analysis-of-Nitsches-and-discontinuous-Galerkin-methods] Text (Maity-etal-CMAM-2020-Error-analysis-of-Nitsches-and-discontinuous-Galerkin-methods)
Maity_etal_CMAM_2020_Error_analysis_of_Nitsches_and_discontinuous_Galerkin_methods.pdf
Accepted Author Manuscript
Restricted to Repository staff only until 16 December 2021.

Download (2MB) | Request a copy from the Strathclyde author

    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;