Effect of an efficient numerical integration technique on the element-free Galerkin method

Abstract

The reproducing kernel gradient smoothing integration (RKGSI) is an efficient technique to tackle the integration problem and optimal convergence in meshless methods. In this paper, the effect of the RKGSI on the element-free Galerkin (EFG) method is studied for elliptic boundary value problems with mixed boundary conditions. Theoretical results of smoothed gradients in the RKGSI are provided. Fundamental criteria on how to determine integration points and weights of quadrature rules are established according to necessary algebraic precision. By using the Nitsche's technique to impose Dirichlet boundary condition, the existence, uniqueness and error estimations of the solution of the EFG method with numerical integration are analyzed. Numerical results validate the theoretical analysis and the optimal convergence of the method.