Element free and improved element free galerkin methods for one and two-dimensional potential problems

Abstract

Potential difficulties appears with various physical and engineering problems where functions satisfy a given partial differential equations and particular boundary conditions. From problems which are time independent and involve only space coordinates, one-dimensional examples and bidimensional diffusion equations are studied using two meshless methods: Element Free Galerkin (EFG) and Improved Element free Galerkin(IEFG). These two methods give good results when compared with analytical solution, but IEFG method based on IMLS approximation is in a higher computing speed and precision.