Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 649468, 8 pages
http://dx.doi.org/10.1155/2014/649468
Research Article

Discontinuous Mixed Covolume Methods for Linear Parabolic Integrodifferential Problems

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

Received 4 April 2014; Accepted 17 June 2014; Published 15 July 2014

Academic Editor: Wolfgang Schmidt

Copyright © 2014 Ailing Zhu. 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. V. Thomée and N. Y. Zhang, “Error estimates for semidiscrete finite element methods for parabolic integro-differential equations,” Mathematics of Computation, vol. 53, no. 187, pp. 121–139, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. K. Pani and G. Fairweather, “H1-Galerkin mixed finite element methods for parabolic partial integro-differential equations,” IMA Journal of Numerical Analysis, vol. 22, no. 2, pp. 231–252, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. C. Chen, V. Thomee, and L. B. Wahlbin, “Finite element approximation of a parabolic integro-differential equation with a weakly singular kernel,” Mathematics of Computation, vol. 58, no. 198, pp. 587–602, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  4. A. Zhu and Q. Yang, “Expanded mixed finite element methods for parabolic integro-differential equations,” Journal of Shandong Normal University, vol. 19, no. 2, pp. 10–14, 2004. View at Google Scholar
  5. A. Zhu, Z. Jiang, and Q. Xu, “Expanded mixed covolume method for a linear integro-differential equation of parabolic type,” Numerical Mathematics, vol. 31, no. 3, pp. 193–205, 2009. View at Google Scholar · View at MathSciNet
  6. W. H. Reed and T. R. Hill, “Triangular mesh methods for the neutron transport equation,” Tech. Rep. LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM, USA, 1973. View at Google Scholar
  7. B. Cockburn, S. Hou, and C. W. Shu, “The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case,” Mathematics of Computation, vol. 54, no. 190, pp. 545–581, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  8. B. Cockburn, G. E. Karniaddakis, and C. W. Shu, The Development of Discontinuous Galerkin Methods, Springer, Berlin, Germany, 2000.
  9. B. Cockburn and C. Shu, “The local discontinuous Galerkin method for time-dependent convection-diffusion systems,” SIAM Journal on Numerical Analysis, vol. 35, no. 6, pp. 2440–2463, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. B. Riviere, M. F. Wheeler, and V. Girault, “Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems—part I,” Computational Geosciences, vol. 3, no. 3-4, pp. 337–360, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  11. D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, “Unified analysis of discontinuous Galerkin methods for elliptic problems,” SIAM Journal on Numerical Analysis, vol. 39, no. 5, pp. 1749–1779, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. X. Ye, “A new discontinuous finite volume method for elliptic problems,” SIAM Journal on Numerical Analysis, vol. 42, no. 3, pp. 1062–1072, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. X. Ye, “A discontinuous finite volume method for the Stokes problems,” SIAM Journal on Numerical Analysis, vol. 44, no. 1, pp. 183–198, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. C. Bi and J. Geng, “Discontinuous finite volume element method for parabolic problems,” Numerical Methods for Partial Differential Equations, vol. 26, no. 2, pp. 367–383, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Q. Yang and Z. Jiang, “A discontinuous mixed covolume method for elliptic problems,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2467–2476, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. A. Zhu and Z. Jiang, “Discontinuous mixed covolume methods for parabolic problems,” The Scientific World Journal, vol. 2014, Article ID 867863, 8 pages, 2014. View at Publisher · View at Google Scholar
  17. R. A. Adams, Sobolev Spaces, Academic Press, New York, NY, USA, 1975. View at MathSciNet