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 language | English |
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Pages (from-to) | 179–209 |
Number of pages | 31 |
Journal | Computational Methods in Applied Mathematics |
Volume | 21 |
Issue number | 1 |
Early online date | 16 Dec 2020 |
DOIs | |
Publication status | E-pub ahead of print - 16 Dec 2020 |
Keywords
- non-linear elliptic PDE
- non-homogeneous Dirichlet boundary data
- lower regularity
- Nitsche's methodq