Abstract
In this paper, an adaptive element free Galerkin (EFG) method is presented to solve Poisson equation. In general, element free Galerkin method using moving least square (MLS) approximation needs a background mesh for integration. With the arbitrary polygonal influence domain technique, the shape function of MLS has almost interpolation property, and the Gaussian quadrature points in the background integration element only contribute to the vertices of that element, which enables us to compute the residual based on the background integration element just like the finite element method (FEM). The adaptive procedure based on triangular or tetrahedral background integration elements is then developed for EFG method, in which the residual-based a posteriori error estimation of FEM is used. Numerical examples are provided to illustrate the efficiency of the proposed adaptive EFG method.
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