Moving kriging interpolation and element-free Galerkin method

A new formulation of the element‐free Galerkin (EFG) method is presented in this paper. EFG has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems. However, accurate imposition of essential boundary condi...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2003-01, Vol.56 (1), p.1-11
Main Author: Gu, Lei
Format: Article
Language:English
Subjects:
computational mechanics
Consistency
Convergence
Deltas
Galerkin methods
Interpolation
kriging
Mathematical analysis
Mathematical models
mesh-free method
Shape functions
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Summary:A new formulation of the element‐free Galerkin (EFG) method is presented in this paper. EFG has been extensively popularized in the literature in recent years due to its flexibility and high convergence rate in solving boundary value problems. However, accurate imposition of essential boundary conditions in the EFG method often presents difficulties because the Kronecker delta property, which is satisfied by finite element shape functions, does not necessarily hold for the EFG shape function. The proposed new formulation of EFG eliminates this shortcoming through the moving kriging (MK) interpolation. Two major properties of the MK interpolation: the Kronecker delta property (ϕI(sJ)=δIJ) and the consistency property (∑InϕI(x)=1 and ∑InϕI(x)xIi=xi) are proved. Some preliminary numerical results are given. Copyright © 2002 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.553