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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 934973, 9 pages
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.
- 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.
- 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.
- R. E. Ewing, “Numerical solution of Sobolev partial differential equations,” SIAM Journal on Numerical Analysis, vol. 12, pp. 345–363, 1975.
- 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.
- P. G. Ciarlet, The Finite Element Method for Elliptic Equations, North-Holland, Amsterdam, The Netherlands, 1978.
- I. Babuska, “Error-bounds for finite element method,” Numerische Mathematik, vol. 16, no. 4, pp. 322–333, 1970.
- 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.
- R. S. Falk and J. E. Osborn, “Error estimates for mixed methods,” RAIRO Analyse Numérique, vol. 14, no. 3, pp. 249–277, 1980.
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, vol. 15 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 1991.
- 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.
- 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.
- Z. Chen, “Expandedmixed finite elementmethods for quasilinear second-order elliptic problems,” RAIROMathematical Modelling and Numerical Analysis, vol. 32, no. 4, pp. 500–520, 1998.
- 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.
- 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.
- 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.
- R. A. Adams, Sobolev Spaces, vol. 65, Academic Press, New York, NY, USA, 1975.
- 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.
- 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.
- 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.