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 (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: https://orcid.org/0000-0003-4802-6720 and Nataraj, Neela;-
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Item type: Article ID code: 74999 Dates: DateEvent16 December 2020Published16 December 2020Published Online3 December 2020AcceptedSubjects: 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