Discontinuous Legendre Wavelet Galerkin Method for One-Dimensional Advection-Diffusion Equation

Xiaoyang Zheng, Zhengyuan Wei

College of Mathematics and Statistics, Chongqing University of Technology, Chongqing, China.

DOI: 10.4236/am.2015.69141                

Abstract

This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving one-dimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical fluxes are devised by utilizing the advantages of both the Legendre wavelet bases and discontinuous Galerkin (DG) method. The distinctive features of the proposed method are its simple applicability for a variety of boundary conditions and able to effectively approximate the solution of PDEs with less storage space and execution. The results of a numerical experiment are provided to verify the efficiency of the designed new technique.

Keywords

Advection-Diffusion Equation, Legendre Wavelet, Discontinuous Galerkin Method, Discontinuous Legendre Wavelet Galerkin Method

Conflicts of Interest

The authors declare no conflicts of interest.

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