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Chin. Phys. B, 2009, Vol. 18(10): 4059    DOI: 10.1088/1674-1056/18/10/001
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Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation

Ge Hong-Xiaa, Cheng Rong-Junb, Cheng Yu-Minc
a Faculty of Science, Ningbo University, Ningbo , China; b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Abstract  The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test and trial functions. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for hyperbolic problems needs only the scattered nodes instead of meshing the domain of the problem. It neither requires any element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.
Keywords:  element-free Galerkin (EFG) method      meshless method      hyperbolic problem  
Received:  12 February 2009      Revised:  08 April 2009      Published:  20 October 2009
PACS:  02.70.Dh (Finite-element and Galerkin methods)  
  02.30.Jr (Partial differential equations)  
  02.30.Sa (Functional analysis)  
  02.30.Xx (Calculus of variations)  
  02.60.Cb (Numerical simulation; solution of equations)  
  02.70.Rr (General statistical methods)  
Fund: Project supported by the Natural Science Foundation of Ningbo, China (Grant Nos 2009A610014, 2009A610154, 2008A610020 and 2007A610050).

Cite this article: 

Cheng Rong-Jun, Cheng Yu-Min, Ge Hong-Xia Element-free Galerkin (EFG) method for a kind of two-dimensional linear hyperbolic equation 2009 Chin. Phys. B 18 4059

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