A procedure for approximation of the error in the EFG method

In this paper, we present a procedure to estimate the error in elliptic equations using the element-free Galerkin (EFG) method, whose evaluation is computationally simple and can be readily implemented in existing EFG codes. The estimation of the error works very well in all numerical examples for 2-D potential problems that are presented here, for regular and irregular clouds of points. Moreover, it was demonstrated that this method is very simple in terms of economy and gives a good performance. The results show that the error in EFG approximation may be estimated via the error estimator described in this paper. The quality of the estimation of the error is demonstrated by numerical examples. The implemented procedure of error approximation allows the global energy norm error to be estimated and also gives a good evaluation of local errors. It can, thus, be combined with a full adaptive process of re