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arXiv · 2005.14215

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

Ruma Rani Maity·Apala Majumdar·Neela Nataraj
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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 {\it 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.

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Ruma Rani Maity, Apala Majumdar, Neela Nataraj. 2020-05-28. Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem. https://arxiv.org/abs/2005.14215

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