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

Ruma Rani Maity, Apala Majumdar, Neela Nataraj

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)179–209
Number of pages31
JournalComputational Methods in Applied Mathematics
Volume21
Issue number1
Early online date16 Dec 2020
DOIs
Publication statusE-pub ahead of print - 16 Dec 2020

Keywords

  • non-linear elliptic PDE
  • non-homogeneous Dirichlet boundary data
  • lower regularity
  • Nitsche's methodq

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