Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction-diffusion problems

被引：8
|
作者：
Zhu, Guoqing [1 ]
Chen, Shaochun [2 ]
机构：
[1] Beijing Inst Technol, Sch Sci, Beijing 100081, Peoples R China
[2] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Singular perturbation; Graded meshes; Finite elements; Error estimates; GRADED MESHES; EQUATION; GRIDS;
D O I：
10.1016/j.cam.2010.04.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The numerical approximation by a lower order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving singular perturbation problems. The quasi-optimal order error estimates are proved in the epsilon-weighted H(1)-norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. By using the interpolation postprocessing technique, the global superconvergent error estimates in epsilon-weighted H(1)-norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
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页码：3048 / 3063
页数：16
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