Implementation of essential boundary conditions in a meshless method

Abstract

Accurate imposition of essential boundary conditions is a main drawback in the use of the element-free Galerkin (EFG) method. A way to solve the problem, is to use a constrained variational principle with a penalty function. This new treatment for essential boundary conditions is simple and logical and works very well in all numerical examples for 2-D potential problems that are presented here, considering an approximation close to an interpolation. It is shown that the present constrained variational formulation together with the EFG method and appropriated weighting function exhibit very high accuracy and stability, for regular and irregular grids of nodes. Copyright © 2000 John Wiley & Sons, Ltd.