The early years of meshless methods (1992-1998)

The finite element method (FEM) has come into its own in recent decades, in both academic and industrial circles, and is undoubtedly the most widely used general approach for approximating the solutions of PDEs on complex domains. The finite element method has proven to be a powerful tool, providing accurate results for a wide range of problems and applications. However, its main shortcoming is the frequent and cumbersome need to define an appropriate mesh for the problem under study. Recently, there has been an attempt to bypass this tedious task of mesh elaboration/adaptation through the use of both powerful automatic mesh generators and meshless methods. The latter, while not requiring connectivity information, normally require a background mesh for integration (except when node integration is used). A wide variety of meshless methods have been developed and applied to multiple areas...