Two-level meshless local Petrov Galerkin method for multi-dimensional nonlinear convection–diffusion equation based on radial basis function

Abstract

In this article, a two-level meshless local Petrov Galerkin method (MLPG) is proposed to analyze nonlinear convection–diffusion equation based on the radial basis function (RBF) collocation method. Two-level method is employed to save the computation time, solving one small linearized convection–diffusion equation in a coarse nodal distribution by Newton iterative scheme and then processing one linear equation on a fine nodal distribution. The convergence analysis for the MLPG method and the two-level method is proven by applying the RBF interpolation method. Finally, the numerical examples provide a sufficient support and show that the proposed method is efficient for solving nonlinear convection–diffusion equation.

Acknowledgments

The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this article.

Additional information

Funding

This work is in parts supported by the Excellent Doctor Innovation Program of Xinjiang University (No. XJUBSCX-2017006), the NSF of Xinjiang Province (No. 2016D01C058), the Research Fund from Key Laboratory of Xinjiang Province (No. 2017D04030) and the NSF of China (No. 11671345, No. 11861054).