Weight Functions Analysis in Elastostatic Problems for Meshless Element Free Galerkin Method

Weight functions of the Moving Least Square (MLS) approximation are the key to solve EDPs’ problems by Element Free Galerkin Method (EFGM). That is the reason why it is so important to use the best weight function for each case. This paper contains a systematic analysis of the most common weight functions used in solving elastostatics problems by meshless EFGM. This analysis comprises the influence of the main parameters and their effect on the accuracy of the weight functions on the solution of the problems studied. The referred accuracy is set by calculating the error of the numerical solution versus the actual result, in terms of standard energy norm. However, it is not always the best function the one that solves the problem with the minimum error, but the one that does it with the lowest computational cost. A computational cost analysis method is set to let it be quantifiable. This way, an analysis of the error, as previously said, in terms of standard energy norm, versus computational cost will be done, by minimizing this relationship. Therefore, the accurate weight function is determined at each case analyzed. In the spirit of letting the essential concepts be explained, some numerical examples are provided in the field of Elastostatics.