A Splitting Positive Definite Mixed Element Method for Second-Order Hyperbolic Equations

被引：32
作者：
Zhang, Jiansong [1 ]
Yang, Danping [2 ]
机构：
[1] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Shandong, Peoples R China
[2] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 25卷 / 03期
关键词：
convergence analysis; hyperbolic equation; mixed finite element; splitting positive definite system; FINITE-ELEMENTS;
D O I：
10.1002/num.20363
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we establish a new mixed finite element procedure, in which the mixed element system is symmetric positive definite, to solve the second-order hyperbolic equations. The convergence of the mixed element methods with continuous- and discrete-time scheme is proved. And the corresponding error estimates are given. Finally some numerical results are presented. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 622-636, 2009
引用
收藏
页码：622 / 636
页数：15
相关论文
共 16 条
[1]  
Adams R., 2003, Pure and Applied Mathematics, V140
[2]  
[Anonymous], 1977, MATH ASPECTS FINITE
[3]   ERROR ESTIMATES FOR FINITE-ELEMENT METHODS FOR 2ND ORDER HYPERBOLIC EQUATIONS [J].
BAKER, GA .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1976, 13 (04) :564-576
[4]   2 FAMILIES OF MIXED FINITE-ELEMENTS FOR 2ND ORDER ELLIPTIC PROBLEMS [J].
BREZZI, F ;
DOUGLAS, J ;
MARINI, LD .
NUMERISCHE MATHEMATIK, 1985, 47 (02) :217-235
[5]   MIXED FINITE-ELEMENTS FOR 2ND-ORDER ELLIPTIC PROBLEMS IN 3 VARIABLES [J].
BREZZI, F ;
DOUGLAS, J ;
DURAN, R ;
FORTIN, M .
NUMERISCHE MATHEMATIK, 1987, 51 (02) :237-250
[6]  
BREZZI F, 1987, RAIRO-MATH MODEL NUM, V21, P581
[7]  
CHEN Y, 2000, SYSTEMS ENG ELECT, V22, P69
[8]  
Ciarlet Philippe G., 2002, Finite Element Method for Elliptic Problems
[9]   A PRIORI ESTIMATES FOR MIXED FINITE-ELEMENT METHODS FOR THE WAVE-EQUATION [J].
COWSAR, LC ;
DUPONT, TF ;
WHEELER, MF .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1990, 82 (1-3) :205-222
[10]   L2-ESTIMATES FOR GALERKIN METHODS FOR SECOND-ORDER HYPERBOLIC EQUATIONS [J].
DUPONT, T .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1973, 10 (05) :880-889
12