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The Element Free Galerkin (EFG) method is a mesh less method for solving partial differential equations in which the trial and test functions employed in the discretization process result from moving least square interpolations (weak form of the variation AL principle). In this paper, the EFG method for solving problems in least-statics {1-D, 2-D) is developed and numerically implemented. The present method is a mesh less method, as it does not need a "finite element mesh" and it is only composed by the particles with theirs "compact support" (the influence domain) in the whole domain. Specially, the shape functions are not satisfying the Kronecker delta property, therefore, in this paper, we must enforce the essential boundary conditions by the Lagrangian multipliers method. Finally, several numerical examples are presented to illustrate the performance of the EFG method. The results are compared with the other method (EFM) and also with the analytic solutions. It shows that the EFG method gives the good effectiveness of the proposed error estimator in the global energy norm and the high rates of convergence with the size of the "compact support".

On the element free Galerkin method in the static-analysis for the 2-D elastic-linear problem