Local ultraconvergence of linear and bilinear finite element method for second order elliptic problems

被引：2

作者：

He, Wen-ming ^{[1
]}

Lin, Runchang ^{[2
]}

Zhang, Zhimin ^{[3
,4
]}

机构：

[1] Lingnan Normal Univ, Dept Math, Zhanjiang 524000, Guangdong, Peoples R China

[2] Texas A&M Int Univ, Dept Math & Phys, Laredo, TX 78041 USA

[3] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[4] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 372卷

基金：

中国国家自然科学基金;

关键词：

Ultraconvergence; Finite element; Interpolation; Richardson extrapolation; Local symmetry theory; Green function; RICHARDSON EXTRAPOLATION; PATCH RECOVERY; SUPERCONVERGENCE; MESHES; ERROR;

D O I：

10.1016/j.cam.2020.112715

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, local ultraconvergence in gradient of the bilinear and linear finite element solutions to two-dimensional second order elliptic problems has been investigated. Special interpolation postprocessing algorithms of numerical solutions by Richardson extrapolation have been developed. The local symmetry theory and estimates of discrete Green functions are used in the analysis. Numerical experiments are provided to confirm the theoretical findings. Published by Elsevier B.V.

引用

页数：19

共 39 条

[1]

[Anonymous], 2001, The Finite Element Method and Its Reliability

[2] A NEW APPROACH TO RICHARDSON EXTRAPOLATION IN THE FINITE ELEMENT METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS [J].

Asadzadeh, M. ;

Schatz, A. H. ;

Wendland, W. .

MATHEMATICS OF COMPUTATION, 2009, 78 (268) :1951-1973

[3] Improving the rate of convergence of high-order finite elements on polyhedra I:: A priori estimates [J].

Bacuta, C ;

Nistor, V ;

Zikatanov, LT .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2005, 26 (06) :613-639

[4] ASYMPTOTIC ERROR EXPANSION AND RICHARDSON EXTRAPOLATION FOR LINEAR FINITE-ELEMENTS [J].

BLUM, H ;

LIN, Q ;

RANNACHER, R .

NUMERISCHE MATHEMATIK, 1986, 49 (01) :11-37

[5]

Chen C., 1995, High Accuracy Theory of Finite Element Methods

[6]

Chen C., 2001, Structure theory of superconvergence of finite elements

[7] LINEAR FINITE ELEMENT SUPERCONVERGENCE ON SIMPLICIAL MESHES [J].

Chen, Jie ;

Wang, Desheng ;

Du, Qiang .

MATHEMATICS OF COMPUTATION, 2014, 83 (289) :2161-2185

[8]

Chen YP, 2016, J SCI COMPUT, V69, P28, DOI 10.1007/s10915-016-0187-8

[9] Ultraconvergence of high order FEMs for elliptic problems with variable coefficients [J].

He, Wen-ming ;

Zhang, Zhimin ;

Zou, Qingsong .

NUMERISCHE MATHEMATIK, 2017, 136 (01) :215-248

[10] ULTRACONVERGENCE OF FINITE ELEMENT METHOD BY RICHARDSON EXTRAPOLATION FOR ELLIPTIC PROBLEMS WITH CONSTANT COEFFICIENTS [J].

He, Wen-Ming ;

Lin, Runchang ;

Zhang, Zhimin .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (04) :2302-2322

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