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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 934973, 9 pages
http://dx.doi.org/10.1155/2013/934973
Research Article

Expanded Mixed Finite Element Method for the Two-Dimensional Sobolev Equation

1School of Mathematics, Shandong University, Jinan 250100, China
2School of Science, Shandong Jianzhu University, Jinan 250101, China

Received 23 April 2013; Revised 7 June 2013; Accepted 7 June 2013

Academic Editor: Carlos Conca

Copyright © 2013 Qing-li Zhao 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.

Linked References

  1. N. Li, F. Gao, and T. Zhang, “An expanded mixed finite element method for Sobolev equation,” Journal of Computational Analysis and Applications, vol. 15, no. 3, pp. 535–543, 2013.
  2. T. Sun, “A Godunov-mixed finite element method on changing meshes for the nonlinear Sobolev equations,” Abstract and Applied Analysis, vol. 2012, Article ID 413718, 19 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. E. Ewing, “Numerical solution of Sobolev partial differential equations,” SIAM Journal on Numerical Analysis, vol. 12, pp. 345–363, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. D. Shi and Y. Zhang, “High accuracy analysis of a new nonconforming mixed finite element scheme for Sobolev equations,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3176–3186, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. G. Ciarlet, The Finite Element Method for Elliptic Equations, North-Holland, Amsterdam, The Netherlands, 1978. View at MathSciNet
  6. I. Babuska, “Error-bounds for finite element method,” Numerische Mathematik, vol. 16, no. 4, pp. 322–333, 1970. View at MathSciNet
  7. F. Brezzi, “On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers,” RAIRO Mathematical Modelling and Numerical Analysis, vol. 8, no. 2, pp. 129–151, 1974. View at Zentralblatt MATH · View at MathSciNet
  8. R. S. Falk and J. E. Osborn, “Error estimates for mixed methods,” RAIRO Analyse Numérique, vol. 14, no. 3, pp. 249–277, 1980. View at Zentralblatt MATH · View at MathSciNet
  9. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, vol. 15 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. E. Roberts and J. M. Thomas, “Mixed and hybrid methods,” in Handbook of Numerical Analysis, vol. 2, pp. 523–639, North-Holland, Amsterdam, The Netherlands, 1991. View at Zentralblatt MATH · View at MathSciNet
  11. Z. Chen, “Expanded mixed finite element methods for linear second-order elliptic problems. I,” RAIRO Mathematical Modelling and Numerical Analysis, vol. 32, no. 4, pp. 479–499, 1998. View at Zentralblatt MATH · View at MathSciNet
  12. Z. Chen, “Expandedmixed finite elementmethods for quasilinear second-order elliptic problems,” RAIROMathematical Modelling and Numerical Analysis, vol. 32, no. 4, pp. 500–520, 1998.
  13. L. Guo and H. Z. Chen, “An expanded characteristic-mixed finite element method for a convection-dominated transport problem,” Journal of Computational Mathematics, vol. 23, no. 5, pp. 479–490, 2005. View at Zentralblatt MATH · View at MathSciNet
  14. W. Liu, H. X. Rui, and H. Guo, “A two-grid method with expanded mixed element for nonlinear reaction-diffusion equations,” Acta Mathematicae Applicatae Sinica (English Series), vol. 27, no. 3, pp. 495–502, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. H. Che, Z. Zhou, and Z. Jiang, “H1-Galerkin expanded mixed finite element methods for nonlinear pseudo-parabolic integro-differential equations,” Numerical Methods for Partial Differential Equations, vol. 29, no. 3, pp. 799–817, 2013.
  16. R. A. Adams, Sobolev Spaces, vol. 65, Academic Press, New York, NY, USA, 1975. View at MathSciNet
  17. P. A. Raviart and J. M. Thomas, “A mixed finite element method for 2nd order elliptic problems,” in Mathematical Aspects of Finite Element Methods, vol. 606 of Lecture Notes in Mathematics, pp. 292–315, Springer, Berlin, Germany, 1977. View at Zentralblatt MATH · View at MathSciNet
  18. F. Brezzi, J. Douglas Jr., and L. D. Marini, “Two families of mixed finite elements for second order elliptic problems,” Numerische Mathematik, vol. 47, no. 2, pp. 217–235, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. F. Brezzi, J. Douglas Jr., M. Fortin, and L. D. Marini, “Efficient rectangular mixed finite elements in two and three space variables,” RAIRO Mathematical Modelling and Numerical Analysis, vol. 21, no. 4, pp. 581–604, 1987. View at Zentralblatt MATH · View at MathSciNet