About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 351619, 11 pages
http://dx.doi.org/10.1155/2013/351619
Research Article

The Upwind Finite Volume Element Method for Two-Dimensional Burgers Equation

School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China

Received 15 October 2012; Accepted 8 January 2013

Academic Editor: Xiaodi Li

Copyright © 2013 Qing Yang. 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.

Linked References

  1. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics 1, Springer, Berlin, Germany, 2nd edition, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. E. D. de Goede and J. H. M. ten Thije Boonkkamp, “Vectorization of the odd-even hopscotch scheme and the alternating direction implicit scheme for the two-dimensional Burgers equations,” SIAM Journal on Scientific and Statistical Computing, vol. 11, no. 2, pp. 354–367, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. F. Lu, B. L. Zhang, and T. Xu, “AGE method for two-dimensional Burgers equation and parallel computing,” Chinese Journal of Computational Physics, vol. 15, pp. 225–233, 1998.
  4. R. H. Li, Z. Y. Chen, and W. Wu, Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods, CRC, Boca Raton, Fla, USA, 2000.
  5. Z. Q. Cai and S. McCormick, “On the accuracy of the finite volume element method for diffusion equations on composite grids,” SIAM Journal on Numerical Analysis, vol. 27, no. 3, pp. 636–655, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Z. Q. Cai, J. Mandel, and S. McCormick, “The finite volume element method for diffusion equations on general triangulations,” SIAM Journal on Numerical Analysis, vol. 28, no. 2, pp. 392–402, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z. Q. Cai, “On the finite volume element method,” Numerische Mathematik, vol. 58, no. 7, pp. 713–735, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. Ewing, R. Lazarov, and Y. Lin, “Finite volume element approximations of nonlocal reactive flows in porous media,” Numerical Methods for Partial Differential Equations, vol. 16, no. 3, pp. 285–311, 2000. View at Zentralblatt MATH · View at MathSciNet
  9. T. Zhang, H. Zhong, and J. Zhao, “A full discrete two-grid finite-volume method for a nonlinear parabolic problem,” International Journal of Computer Mathematics, vol. 88, no. 8, pp. 1644–1663, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. T. Zhang, “The semidiscrete finite volume element method for nonlinear convection-diffusion problem,” Applied Mathematics and Computation, vol. 217, no. 19, pp. 7546–7556, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. Liang, “Upwind generalized difference schemes for convection-diffusion equations,” Acta Mathematicae Applicatae Sinica, vol. 13, no. 4, pp. 456–466, 1990. View at MathSciNet
  12. D. Liang, “A kind of upwind schemes for convection diffusion equations,” Mathematica Numerica Sinica, vol. 13, pp. 133–141, 1991.
  13. R. Scholz, “Optimal L-estimates for a mixed finite element method for second order elliptic and parabolic problems,” Calcolo, vol. 20, no. 3, pp. 355–377, 1983. View at Publisher · View at Google Scholar · View at MathSciNet