MLPG method based on moving kriging interpolation for solving convection–diffusion equations with integral condition

Abstract

A formulation of the meshless local Petrov–Galerkin (MLPG) method based on the moving kriging interpolation (MK) is presented in this paper. The method is used for solving time-dependent convection–diffusion equations in two-dimensional spaces with the Dirichlet, Neumann, and non-local boundary conditions on a square domain. The method is developed based on the moving kriging interpolation method for constructing shape functions which have the Kronecker delta property. In the method, the test function in each sub-domain is chosen as the indicator function. The Crank–Nicolson method is chosen for temporal discretization. Two test problems are presented which demonstrate the easiness and accuracy of this method as shown by the relative error.

Keywords

• Convection–diffusion equations
• Crank–Nicolson
• Moving kriging interpolation
• MLPG
• Integral condition