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.

引用

页码：2833 / 2844

页数：12

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