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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 175904, 7 pages
http://dx.doi.org/10.1155/2013/175904
Research Article

A Fully Discrete Symmetric Finite Volume Element Approximation of Nonlocal Reactive Flows in Porous Media

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

Received 9 November 2012; Accepted 30 December 2012

Academic Editor: J. Jiang

Copyright © 2013 Zhe Yin and Qiang Xu. 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. J. H. Cushman and T. R. Ginn, “Nonlocal dispersion in media with continuously evolving scales of heterogeneity,” Transport in Porous Media, vol. 13, no. 1, pp. 123–138, 1993. View at Publisher · View at Google Scholar · View at Scopus
  2. J. H. Cushman, B. X. Hu, and F. Deng, “Nonlocal reactive transport with physical and chemical heterogeneity: localization errors,” Water Resources Research, vol. 31, no. 9, pp. 2219–2237, 1995. View at Publisher · View at Google Scholar · View at Scopus
  3. G. Dagan, “The significance of heterogeneity of evolving scales to transport in porous formations,” Water Resources Research, vol. 30, no. 12, pp. 3327–3336, 1994. View at Scopus
  4. V. V. Shelukhin, “A non-local in time model for radionuclides propagation in Stokes fluids, dynamics of fluids with free boundaries,” Siberian Branch of the Russian Academy of Sciences, Institute of Hydrodynamics, vol. 107, pp. 180–193, 1993.
  5. M. Renardy, W. J. Hrusa, and J. A. Nohel, Mathematical Problems in Viscoelasticity, vol. 35, Longman Scientific and Technical, Essex, UK, 1987. View at MathSciNet
  6. W. Allegretto, Y. Lin, and A. Zhou, “A box scheme for coupled systems resulting from microsensor thermistor problems,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 5, no. 1–4, pp. 209–223, 1999. View at Zentralblatt MATH · View at MathSciNet
  7. J. R. Cannon and Y. Lin, “Nonclassical H1-projection and Galerkin methods for nonlinear parabolic integro-differential equations,” Calcolo, vol. 25, no. 3, pp. 187–201, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Y. P. Lin, V. Thomée, and L. B. Wahlbin, “Ritz-Volterra projections to finite-element spaces and applications to integrodifferential and related equations,” SIAM Journal on Numerical Analysis, vol. 28, no. 4, pp. 1047–1070, 1995. View at Zentralblatt MATH · View at MathSciNet
  9. Y. P. Lin, “On maximum norm estimates for Ritz-Volterra projection with applications to some time dependent problems,” Journal of Computational Mathematics, vol. 15, no. 2, pp. 159–178, 1997. View at Zentralblatt MATH · View at MathSciNet
  10. I. H. Sloan and V. Thomée, “Time discretization of an integro-differential equation of parabolic type,” SIAM Journal on Numerical Analysis, vol. 23, no. 5, pp. 1052–1061, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Zhang, “The stability and approximation properties of Ritz-Volterra projection and application. I,” Numerical Mathematics. English Series, vol. 6, no. 1, pp. 57–76, 1997. View at Zentralblatt MATH · View at MathSciNet
  12. V. Thomée and L. B. Wahlbin, “Long-time numerical solution of a parabolic equation with memory,” Mathematics of Computation, vol. 62, no. 206, pp. 477–496, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. E. Bank and D. J. Rose, “Some error estimates for the box method,” SIAM Journal on Numerical Analysis, vol. 24, no. 4, pp. 777–787, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. 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
  15. 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
  16. W. Hackbusch, “On first and second order box schemes,” Computing, vol. 41, no. 4, pp. 277–296, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. Huang and S. Xi, “On the finite volume element method for general self-adjoint elliptic problems,” SIAM Journal on Numerical Analysis, vol. 35, no. 5, pp. 1762–1774, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. R. Li, Z. Chen, and W. Wu, Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods, vol. 226, Marcel Dekker, New York, NY, USA, 2000. View at MathSciNet
  19. I. D. Mishev, “Finite volume methods on Voronoi meshes,” Numerical Methods for Partial Differential Equations, vol. 14, no. 2, pp. 193–212, 1998. View at Zentralblatt MATH · View at MathSciNet
  20. 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
  21. S. Liang, X. Ma, and A. Zhou, “A symmetric finite volume scheme for selfadjoint elliptic problems,” Journal of Computational and Applied Mathematics, vol. 147, no. 1, pp. 121–136, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. EasyMesh web site, http://www-dinma.univ.trieste.it/nirftc/research/easymesh/.