Superconvergence Analysis of Splitting Positive Definite Nonconforming Mixed Finite Element Method for Pseudo-hyperbolic Equations

被引:12
作者
Shi, Dong-yang [1 ]
Tang, Qi-li [1 ,2 ]
机构
[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
[2] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China
基金
中国国家自然科学基金;
关键词
pseudo-hyperbolic equations; splitting positive definite nonconforming mixed finite element method; superclose; superconvergence; SQUARES GALERKIN PROCEDURES; PSEUDOHYPERBOLIC EQUATIONS; LAGRANGIAN-MULTIPLIERS; DIFFUSION PROBLEMS; STOKES EQUATIONS; APPROXIMATION; EXISTENCE; SCHEME; MESHES;
D O I
10.1007/s10255-013-0261-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in parallel to.parallel to(div,h) norm for p and optimal error estimates in L-2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.
引用
收藏
页码:843 / 854
页数:12
相关论文
共 28 条
[21]   Nonconforming mixed finite element approximation to the stationary Navier-Stokes equations on anisotropic meshes [J].
Shi, Dongyang ;
Ren, Jincheng .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (09) :3842-3852
[22]  
Shi DY, 2009, J COMPUT MATH, V27, P299
[23]  
Shi Zhong-ci, 1986, Mathematica Numerica Sinica, V8, P159
[24]  
Wan WM., 1999, ACTA MATH APPL SIN-E, V22, P311
[25]  
YAN N., 2008, Superconvergence Analysis and a Posteriori Error Estimation in Finite Element Methods
[26]   A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media [J].
Yang, DP .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2001, 17 (03) :229-249
[27]  
Yang DP, 2000, MATH COMPUT, V69, P929, DOI 10.1090/S0025-5718-99-01172-2
[28]   A Splitting Positive Definite Mixed Element Method for Second-Order Hyperbolic Equations [J].
Zhang, Jiansong ;
Yang, Danping .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (03) :622-636