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Error estimates of element-free Galerkin method for potential problems. (Chinese. English summary) Zbl 1199.78009
Summary: Error estimates for a moving least-square approximation, which is a method for obtaining the shape function in an element-free Galerkin method, are presented in the Sobolev space $$W^{k,p} (\varOmega)$$ for high dimensional problems. Then, on the basis of element-free Galerkin method for potential problems, error estimates for the element-free Galerkin method for potential problems, in which the essential boundary conditions are enforced by penalty methods, are obtained. The error estimates we present in this paper have optimal order when the nodes and shape functions satisfy certain conditions. From the error analysis, it is shown that the error bound of the potential problem is directly related to the radii of the weight functions. Two numerical examples are also given to verify the conclusions in this paper.

##### MSC:
 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs