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 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 ( ϕ I ( s J )= δ IJ ) and the consistency property (∑ I n ϕ I ( x )=1 and ∑ I n ϕ I ( x ) x Ii = x i ) are proved. Some preliminary numerical results are given.