A superconvergent finite node method for semilinear elliptic problems

Abstract

This paper proposes and analyzes a superconvergent finite node method (SFPM) for meshless solution of semilinear boundary value problems with variable coefficients. Smoothed derivatives of the moving least squares approximation are adopted in the SFPM to achieve the high accuracy and favorable superconvergence. Theoretical accuracy analysis of the SFPM and the traditional FPM is detailedly presented through local truncation error analysis. Some numerical results are provided to demonstrate the superconvergence and theoretical results of the method.