A Comparative Study of Mesh-Free Radial Point Interpolation Method and Moving Least Squares Method-Based Error Estimation in Elastic Finite Element Analysis

Abstract

The mesh-free interpolation method-based recovery of finite element discretization error is presented in this study. Two interpolation schemes, namely radial point interpolation method and moving least squares method, are taken for the recovery of finite element solution error. The global and elemental errors of finite element solution are evaluated in energy norm. The two-dimensional benchmark elastic problems are analysed using triangular/quadrilateral meshing schemes to prove the proposed mesh-free error estimation techniques validity and the effectiveness. The results of the mesh-less interpolation recovery-based error estimation are also compared with mesh-dependent least squares interpolation method-based error estimation. The mesh-free recovery is based on the fitting of a higher-order polynomial to the field variable over a mesh-less patch (radial support domain) using RPI and MLS interpolation method, while the mesh-dependent recovery is based on recovery of the field variable over a patch of nodes surrounding the particular given node using RPI, MLS and LS interpolation method. The study presents the effect of polynomial basis function (LS), polynomial basis function along with radial basis function (RPI)-based interpolation method and weighted polynomial basis function (MLS) on the recovery of finite element solution error. The quality of error estimation under different interpolation schemes is compared in terms of convergence characteristics, local/global effectivity, error distribution patterns and adaptively refined meshes. It can be concluded that weighting function of least squares interpolation affects considerably the mesh-free error estimation.