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

Author

Listed:
  • Ping Zhang
  • Xiaohua Zhang
  • Laizhong Song

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.

Suggested Citation

  • Ping Zhang & Xiaohua Zhang & Laizhong Song, 2016. "Variational Multiscale Element Free Galerkin Method Coupled with Low‐Pass Filter for Burgers’ Equation with Small Diffusion," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:1836978
    DOI: 10.1155/2016/1836978
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    References listed on IDEAS

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    1. Nguyen, Vinh Phu & Rabczuk, Timon & Bordas, Stéphane & Duflot, Marc, 2008. "Meshless methods: A review and computer implementation aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 763-813.
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