A GE/BC imbedded local polynomial collocation method for two dimensional multivariable problems

Abstract In this study, a meshless numerical method for 2D problems with 2 variables coupled together in 2 partial differential equations (PDEs) is proposed. This method employs the local polynomial approximation with the weighted-least-squares (WLS) approach. A very distinguishing feature of this method from other collocation methods is the governing equations are satisfied at boundary nodes as well as the boundary conditions. By doing so the strong-form collocation method would be more stable. The 2D elasto-statics analysis is chosen for demonstrating the performance. Three test cases are implemented and the results are compared with exact or analytic solutions. Very good agreements are found.