Two-Grid Method for Burgers' Equation by a New Mixed Finite Element Scheme

被引：10

作者：

Hu, Xiaohui ^{[1
]}

Huang, Pengzhan ^{[1
]}

Feng, Xinlong ^{[1
]}

机构：

[1] Xinjiang Univ, Urumqi 830046, Peoples R China

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2014年 / 19卷 / 01期

基金：

中国博士后科学基金;

关键词：

Burgers' equation; two-grid method; stable conforming finite element; Crank-Nicolson scheme; inf sup condition; SEMILINEAR ELLIPTIC-EQUATIONS; TIME-STEPPING STRATEGY; DIFFUSION EQUATIONS;

D O I：

10.3846/13926292.2014.892902

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we present two-grid stable mixed finite element method for the 2D Burgers' equation approximated by the P-0(2) - P-1 pair which satisfies the inf-sup condition. This method consists in dealing with the nonlinear system on a coarse mesh with width H and the linear system on a fine mesh with width h << H by using Crank-Nicolson time-discretization scheme. Our results show that if we choose H-2 = h this method can achieve asymptotically optimal approximation. Error estimates are derived in detail. Finally, numerical experiments show the efficiency of our proposed method and justify the theoretical results.

引用

页码：1 / 17

页数：17

共 29 条

[1]

[Anonymous], 1977, MATH ASPECTS FINITE

[2]

Bressan N., 1987, CALCOLO, V23, P265

[3]

Brezzi F., 1991, Mixed and Hybrid Finite Element Methods, V15

[4]

CADWELL J, 1981, APPL MATH MODEL, V5, P189

[5]

CHEN Y., 2009, ADV APPL MATH MECH, V1, P1, DOI DOI 10.1016/J.BBRC.2009.05.048

[6] A two-grid method for expanded mixed finite-element solution of semilinear reaction-diffusion equations [J].

Chen, YP ;

Huang, YQ ;

Yu, DH .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2003, 57 (02) :193-209

[7]

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

[8]

DAWSON CN, 1994, CONT MATH, V180, P191

[9]

DOUGLAS J, 1983, RAIRO-ANAL NUMER-NUM, V17, P17

[10]

DOUGLAS J, 1985, MATH COMPUT, V44, P39, DOI 10.1090/S0025-5718-1985-0771029-9

← 1 2 3 →