H1-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation

被引：14

作者：

He, Yinnian ^{[1
]}

Feng, Xinlong ^{[2
]}

机构：

[1] Xi An Jiao Tong Univ, Ctr Computat Geosci, Sch Math & Stat, Xian 710049, Peoples R China

[2] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2013年 / 3卷 / 02期

基金：

中国博士后科学基金;

关键词：

Finite element method; finite difference method; finite volume method; Poisson equation; stability and convergence; FINITE-VOLUME METHODS; ELEMENT;

D O I：

10.4208/eajam.180313.300513a

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain the coefficient matrices of the finite element (FE), finite volume (FV) and finite difference (FD) methods based on P-1-conforming elements on a quasi-uniform mesh, in order to approximately solve a boundary value problem involving the elliptic Poisson equation. The three methods are shown to possess the same H-1-stability and convergence. Some numerical tests are made, to compare the numerical results from the three methods and to review our theoretical results.

引用

页码：154 / 170

页数：17

共 18 条

[1]

[Anonymous], MODERN NUMERICAL MET

[2]

[Anonymous], 2003, ITERATIVE METHODS SP, DOI DOI 10.1137/1.9780898718003

[3] SOME ERROR-ESTIMATES FOR THE BOX METHOD [J].

BANK, RE ;

ROSE, DJ .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (04) :777-787

[4] Convergence of a compact scheme for the pure streamfunction formulation of the unsteady Navier-Stokes system [J].

Ben-Artzi, Matania ;

Croisille, Jean-Pierre ;

Fishelov, Dalia .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (05) :1997-2024

[5]

CAI ZQ, 1991, NUMER MATH, V58, P713

[6] A NEW CLASS OF HIGH ORDER FINITE VOLUME METHODS FOR SECOND ORDER ELLIPTIC EQUATIONS [J].

Chen, Long .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 47 (06) :4021-4043

[7]

CIARLET P. G., 2002, Classics in Appl. Math., V40

[8] On the accuracy of the finite volume element method based on piecewise linear polynomials [J].

Ewing, RE ;

Lin, T ;

Lin, YP .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (06) :1865-1888

[9] ON 1ST AND 2ND ORDER BOX SCHEMES [J].

HACKBUSCH, W .

COMPUTING, 1989, 41 (04) :277-296

[10]

Li R., 2000, GEN DIFFERENCE METHO

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