Element-free Galerkin method for a kind of KdV equation

doi:10.1088/1674-1056/19/6/060201

Abstract The present paper deals with the numerical solution of the third-order nonlinear KdV equation using the element-free Galerkin (EFG) method which is based on the moving least-squares approximation. A variational method is used to obtain discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for KdV equations needs only scattered nodes instead of meshing the domain of the problem. It does not require any element connectivity and does not suffer much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for the KdV equation is investigated by two numerical examples in this paper.

Keywords: element-free Galerkin method meshless method KdV equation

Received: 26 May 2009
Revised: 28 December 2009
Accepted manuscript online:

PACS:	02.70.Dh	(Finite-element and Galerkin methods)
	02.30.Xx	(Calculus of variations)
	02.70.Rr	(General statistical methods)

Fund: Project supported by the Natural Science Foundation of Ningbo City (Grant No.~2009A610014), the Natural Science Foundation of Zhejiang Province (Grant No.~Y6090131), and the Research Foundation of Ningbo University of Technology (Grant No.~2008004).

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Wang Ju-Feng(王聚丰), Sun Feng-Xin(孙凤欣), and Cheng Rong-Jun(程荣军) Element-free Galerkin method for a kind of KdV equation 2010 Chin. Phys. B 19 060201

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Element-free Galerkin method for a kind of KdV equation

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