An error estimator and adaptivity based on basis coefficient-vector field of element-free Galerkin method

摘要

In this paper, an error estimator for element-free Galerkin (EFG) method has been proposed. Since meshfree methods do not require a structured mesh or a sense of nodal belongingness, the methods offer the advantage of insertion, deletion, and redistribution of nodes adaptively in the problem domain. The trial function of the field variable is constructed entirely in terms of consistent basis functions and its associated coefficient. The proposed error estimator is based on the nodal coefficient-vector of the basis functions that are used to construct the trial function. After obtaining the nodal coefficient-vector from EFG solution, an attempt is made to recover the best nodal coefficient-vector based on the reduced domain of influence [Chung and Belytschko (1998)], which is sufficient enough to maintain the regularity of the EFG moment matrix and also ensuring that sufficient influencing nodes are present in all the four quadrants defined at the sample node. The vertices of the Voronoi polygon of the critical error nodes are considered as potential neighborhood and new nodes are inserted at the vertices. Numerical studies have been carried out to illustrate the performance of the proposed methodology of error estimator and adaptivity.