A Novel Meshless Element Method for Elliptic Equation

Abstract

Meshless method based on strong form has the advantages of high computational speed and convenient application, but it suffers low accuracy and instability. In this paper, we propose a meshless virtual element method (VEM) based on strong-form to promote accuracy and instability. Virtual element is built around each node for establishing local function, which used to calculate the derivative of shape function. The optimal selection of point-cloud with adaptive algorithm is proposed to balance the stability and accuracy of interpolation. Numerical simulation demonstrates that VEM has improvement in stability compared with other conventional strong-form method, just needing additional small calculation. and surpass finite element method (FEM) in accuracy and the ability for catching high gradient change.