论文标题
Nitsche的错误分析和不连续的Galerkin方法减少了Landau-De Gennes问题
Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem
论文作者
论文摘要
我们研究了一个半线性椭圆形偏微分方程的系统，具有较低的立方非线性项和不均匀的Dirichlet边界条件，在降低的Landau-DE基因框架内，与二维Bistable液晶器件有关。主要结果是（i）在精确解决方案的较小的规律性假设下，在尼特切（Nitsche）的和不连续的盖尔金（Galerkin）框架内，对能量规范的先验误差估计，以及（ii）在两种情况下进行足够大的惩罚参数，以及足够好的大惩罚参数的可靠，有效{\ IT后验分析。验证理论结果的数值示例分别显示。
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.
