Supercloseness of continuous interior penalty method for convection-diffusion problems with characteristic layers
Supercloseness of continuous interior penalty method for convection-diffusion problems with characteristic layers
复制标题
具有特征层的对流扩散问题的连续内罚法的超逼近性
DOI：
10.1016/j.cma.2017.03.013
复制
发表时间：
2017
影响因子：
7.2
通讯作者：
Stynes Martin
中科院分区：
文献类型：
--
作者：
Zhang Jin;Stynes Martin
使用连续内罚（CIP）方法和矩形希什金网格上的分段双线性来解决单位正方形上提出的奇异扰动对流扩散问题。详细分析证明了 CIP 方法的新稳定性界限，其规范比通常的 CIP 规范更强。此界限为 CIP 方法提供了新的超接近结果：计算出的解显示为二阶（高达对数因子），以新的强范数收敛于真实解的分段双线性插值。作为推论，我们在 CIP 解的 L 2 范数中获得了几乎最优阶收敛到真实解。数值实验说明了这些理论结果。
A singularly perturbed convection–diffusion problem posed on the unit square is solved using a continuous interior penalty (CIP) method with piecewise bilinears on a rectangular Shishkin mesh. A detailed analysis proves a new stability bound for the CIP method, in a norm that is stronger than the usual CIP norm. This bound enables a new supercloseness result for the CIP method: the computed solution is shown to be second order (up to a logarithmic factor) convergent in the new strong norm to the piecewise bilinear interpolant of the true solution. As a corollary one obtains almost optimal order convergence in the L 2 norm of the CIP solution to the true solution. Numerical experiments illustrate these theoretical results.