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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 1836978, 12 pages
http://dx.doi.org/10.1155/2016/1836978
Research Article

Variational Multiscale Element Free Galerkin Method Coupled with Low-Pass Filter for Burgers’ Equation with Small Diffusion

College of Science, China Three Gorges University, Yichang 443002, China

Received 22 October 2015; Revised 27 January 2016; Accepted 2 February 2016

Academic Editor: Stephen C. Anco

Copyright © 2016 Ping Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Variational multiscale element free Galerkin (VMEFG) method is applied to Burgers’ equation. It can be found that, for the very small diffusivity coefficients, VMEFG method still suffers from instability in the presence of boundary or interior layers. In order to overcome this problem, the high order low-pass filter is used to smooth the solution. Three test examples with very small diffusion are presented and the solutions obtained are compared with exact solutions and some other numerical methods. The numerical results are found in which the VMEFG coupled with low-pass filter works very well for Burgers’ equation with very small diffusivity coefficients.