A priori and a posteriori analysis of the meshless Galerkin boundary node method for three-dimensional elasticity

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• 作者：Xiaolin Li ; ^{lxlmath@163.com}
• 关键词：Meshless method ; Galerkin boundary node method ; Elasticity ; A priori error estimates ; A posteriori error estimates ; Adaptive algorithm
• 刊名：Engineering Analysis with Boundary Elements
• 出版年：2012
• 期刊代码：51_09557997
• 类别：et
• 出版时间：June, 2012
• 卷：36
• 期：6
• 页码：993-1004
• 文件大小：1742 K

摘要

The meshless Galerkin boundary node method is presented in this paper for boundary-only analysis of three-dimensional elasticity problems. In this method, boundary conditions can be implemented directly and easily despite the employed moving least-squares shape functions lack the delta function property, and the resulting system matrices are symmetric and positive definite. A priori error estimates and the consequent rate of convergence are presented. A posteriori error estimates are also provided. Reliable and efficient error estimators and an efficient and convergent adaptive meshless algorithm are then derived. Numerical examples showing the efficiency of the method, confirming the theoretical properties of the error estimates, and illustrating the capability of the adaptive algorithm, are reported.