MLS(Moving Least Square)-based finite elements and their applications

Abstract

A new class of finite elements based on MLS(Moving Least Square) approximation are proposed. The presented elements have an arbitrary number of nodes at the element edges in master domain with the aid of MLS-approximation. Although its shape functions are derived from MLS-approximations, they maintain the point interpolation by making a special choice of the domain of influence of each node and polynomial basis. Due to this feature, numerical integration is straightforwardly accomplished by Gaussian integration. Two and three dimensional useful elements are devised for nonmatching meshes which are difficult and inefficient in the conventional finite elements methods. The present scheme extends trial function space to the space in which $C^1$ continuity are relaxed. For the verification of performance and efficiency, several examples including nonmatching meshes, adaptive mesh refinement and contact problems are demonstrated.