A meshless superconvergent stabilized collocation method for linear and nonlinear elliptic problems with accuracy analysis

Abstract

The stabilized collocation method (SCM) is a promising meshless collocation method that can overcome the instability defects in the classical direct collocation method. To improve the performance of the SCM, a superconvergent stabilized collocation method (SSCM) is developed in this paper for linear and nonlinear elliptic problems through the use of the moving least squares (MLS) approximation and its smoothed derivatives. Accuracy of the SSCM and the SCM is analyzed with an emphasis on the influence of boundary conditions, and precise error measures are presented for different types of boundary conditions. Numerical results validate the superconvergence of the SSCM and confirm the theoretical analysis.