Adaptive refinement analysis for the coupled boundary element method-reproducing kernel particle method

Abstract

The boundary element method (BEM) and the meshless methods have been applied to solve many engineering problems. It is often desirable and beneficial to combine the BEM and meshless methods in order to exploit their advantages while evading their disadvantages. In this study, a review is first conducted to provide background on the a posteriori error estimation and adaptive refinement for the BEM, the meshless methods and the coupled methods for the BEM and the meshless methods. Based on the formulation of the BEM and the reproducing kernel particle method (RKPM), a new coupled method of the BEM and the RKPM is proposed for two dimensional elastostatic problems. Numerical experiments on four benchmark problems are also carried out to compare the convergence rates of the BEM, the RKPM and the coupled BE-RKPM.