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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 580461, 10 pages
A Rectangular Mixed Finite Element Method with a Continuous Flux for an Elliptic Equation Modelling Darcy Flow
School of Mathematics, Shandong University, Jinan 250100, China
Received 26 March 2013; Accepted 29 May 2013
Academic Editor: Santanu Saha Ray
Copyright © 2013 Xindong Li and Hongxing Rui. 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.
- P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, The Netherlands, 1977.
- V. Girault and P.-A. Raviart, Finite Element Approximations of the Navier-Stokes Equations, vol. 749, Springer, New York, NY, USA, 1979.
- F. Brezzi, J. Douglas, Jr., R. Durán, and M. Fortin, “Mixed finite elements for second order elliptic problems in three variables,” Numerische Mathematik, vol. 51, no. 2, pp. 237–250, 1987.
- F. Brezzi, J. Douglas,, M. Fortin, and L. D. Marini, “Efficient rectangular mixed finite elements in two and three space variables,” Mathematical Modelling and Numerical Analysis, vol. 21, no. 4, pp. 581–604, 1987.
- F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, vol. 15 of Springer Series in Computational Mathematics, Springer, New York, NY, USA, 1991.
- P.-A. Raviart and J. M. Thomas, “A mixed finite element method for 2nd order elliptic problems,” in Mathematical Aspects of the FEM, vol. 606 of Lecture Notes in Mathematics, pp. 292–315, Springer, 1977.
- M. R. Correa and A. F. D. Loula, “Unconditionally stable mixed finite element methods for Darcy flow,” Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 17-18, pp. 1525–1540, 2008.
- A. Masud and T. J. R. Hughes, “A stabilized mixed finite element method for Darcy flow,” Computer Methods in Applied Mechanics and Engineering, vol. 191, no. 39-40, pp. 4341–4370, 2002.
- J. Bear, Dynamics of Fluids in Porous Media, Dover, New York, NY, USA, 1972.
- H. Rui and M. Tabata, “A mass-conservative characteristic finite element scheme for convection-diffusion problems,” Journal of Scientific Computing, vol. 43, no. 3, pp. 416–432, 2010.
- T. Arbogast and M. F. Wheeler, “A family of rectangular mixed elements with a continuous flux for second order elliptic problems,” SIAM Journal on Numerical Analysis, vol. 42, no. 5, pp. 1914–1931, 2005.
- H. D. Han, “An economical finite element scheme for Navier-Stokes equations,” Journal of Computational Mathematics, vol. 5, no. 2, pp. 135–143, 1987.
- H. Han and X. Wu, “A new mixed finite element formulation and the MAC method for the Stokes equations,” SIAM Journal on Numerical Analysis, vol. 35, no. 2, pp. 560–571, 1998.
- H. Han and M. Yan, “A mixed finite element method on a staggered mesh for Navier-Stokes equations,” Journal of Computational Mathematics, vol. 26, no. 6, pp. 816–824, 2008.
- I. Babuška, “Error-bounds for finite element method,” Numerische Mathematik, vol. 16, pp. 322–333, 1971.
- F. Brezzi, “On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers,” vol. 8, no. 2, pp. 129–151, 1974.