Adaptive methodology for the meshless Galerkin boundary node method

The Galerkin boundary node method (GBNM) is a boundary-type meshless method that combines a variational form of boundary integral formulations for governing equations with the moving least-squares approximations for generation of the trial and test functions. In this paper, a posteriori error estimate and an effective adaptive h-refinement procedure are developed in conjunction with the GBNM. The error estimator is based on the difference between numerical solutions obtained using two successive nodal arrangements. The reliability and efficiency of this error estimator and the convergence of this adaptive meshless scheme are verified theoretically. Numerical examples are also given to show the efficiency of the adaptive methodology.