A FINITE ELEMENT METHOD FOR EXTENDED KDV EQUATIONS

被引：7
|
作者：
Karczewska, Anna [1 ]
Rozmej, Piotr [2 ]
Szczecinski, Maciej [1 ]
Boguniewicz, Bartosz [2 ]
机构：
[1] Univ Zielona Gora, Fac Math Comp Sci & Econometr, Szafrana 4a, PL-65516 Zielona Gora, Poland
[2] Univ Zielona Gora, Fac Phys & Astron, Inst Phys, Szafrana 4a, PL-65516 Zielona Gora, Poland
来源：
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE | 2016年 / 26卷 / 03期
关键词：
shallow water wave problem; nonlinear equations; second order KdV equations; finite element method; Petrov-Galerkin method; SLOWLY VARYING BOTTOM; SOLITARY WAVE; RESONANT FLOW; UNIDIRECTIONAL WAVES; ENERGY-CONSERVATION; GALERKIN METHOD; WATER; DERIVATION; FLUID; EVOLUTION;
D O I：
10.1515/amcs-2016-0039
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.
引用
收藏
页码：555 / 567
页数：13
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