Numerical solutions to regularized long wave equation based on mixed covolume method

被引：4

作者：

Fang, Zhi-chao ^{[1
]}

Li, Hong ^{[1
]}

机构：

[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China

来源：

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION | 2013年 / 34卷 / 07期

基金：

美国国家科学基金会;

关键词：

regularized long wave equation; mixed covolume method; fully discrete; optimal error estimate; FINITE-ELEMENT-METHOD; DISPERSIVE WAVES; GALERKIN METHODS; MODEL EQUATIONS; RLW EQUATION;

D O I：

10.1007/s10483-013-1716-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The mixed covolume method for the regularized long wave equation is developed and studied. By introducing a transfer operator gamma (h) , which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.

引用

页码：907 / 920

页数：14

共 17 条

[1] GALERKIN METHODS APPLIED TO SOME MODEL EQUATIONS FOR NONLINEAR DISPERSIVE WAVES [J].

ALEXANDER, ME ;

MORRIS, JL .

JOURNAL OF COMPUTATIONAL PHYSICS, 1979, 30 (03) :428-451

[2] MODEL EQUATIONS FOR LONG WAVES IN NONLINEAR DISPERSIVE SYSTEMS [J].

BENJAMIN, TB ;

BONA, JL ;

MAHONY, JJ .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 272 (1220) :47-+

[3]

Cai Z., 1997, Computational Geosciences, V1, P289, DOI [10.1023/A:1011577530905, DOI 10.1023/A:1011577530905]

[4] Mixed covolume methods for elliptic problems on triangular grids [J].

Chou, SH ;

Kwak, DY ;

Vassilevski, PS .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (05) :1850-1861

[5]

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

[6] Galerkin method for the numerical solution of the RLW equation using quintic B-splines [J].

Dag, I ;

Saka, B ;

Irk, D .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 190 (1-2) :532-547

[7]

Elibeck J. C., 1977, J COMPUT PHYS, V23, P63

[8] A B-SPLINE FINITE-ELEMENT METHOD FOR THE REGULARIZED LONG-WAVE EQUATION [J].

GARDNER, LRT ;

GARDNER, GA ;

DAG, I .

COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 1995, 11 (01) :59-68

[9] Least-squares mixed finite element methods for the RLW equations [J].

Gu, Haiming ;

Chen, Ning .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (03) :749-758

[10] THE FOURIER PSEUDOSPECTRAL METHOD WITH A RESTRAIN OPERATOR FOR THE RLW EQUATION [J].

GUO, BY ;

CAO, WM .

JOURNAL OF COMPUTATIONAL PHYSICS, 1988, 74 (01) :110-126

← 1 2 →