Superconvergence of the Crouzeix-Raviart element for elliptic equation

被引：2
|
作者：
Zhang, Yidan [1 ,2 ]
Huang, Yunqing [1 ,2 ]
Yi, Nianyu [1 ,2 ]
机构：
[1] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China
[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2019年 / 45卷 / 5-6期
基金：
中国国家自然科学基金;
关键词：
Crouzeix-Raviart element; Raviart-Thomas element; Nonconforming; Superconvergence; Postprocessing; DISCONTINUOUS GALERKIN METHOD; MIXED FINITE-ELEMENT;
D O I：
10.1007/s10444-019-09714-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a superconvergence result of the Crouzeix-Raviart element method is derived for the second-order elliptic equation on the uniform triangular meshes, in which any two adjacent triangles form a parallelogram. A local weighted averaging post-processing algorithm for the numerical stress is presented. Based on the equivalence between the Crouzeix-Raviart element method and the lowest order Raviart-Thomas element method, we prove that the error between the exact stress and the postprocessed numerical stress is of order h(3/2). Two numerical examples are presented to confirm the theoretical result.
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页码：2833 / 2844
页数：12
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