• 1
    G. A. Baker, Error estimates for finite element methods for second order hyperbolic equations, SIAM J Numer Anal 13(4) (1976), 564576.
  • 2
    Y. Yuan and H. Wang, The discrete-time finite element methods for nonlinear hyperbolic equations and their theoretical analysis, J Comput Math 6(3) (1988), 193204.
  • 3
    L. C. Cowsar, T. F. Dupont, and W. F. Wheeler, A priori estimates for mixed finite element approximations of second-order hyperbolic equations with absorbing boundary conditions, SIAM J Numer Anal 33(2) (1996), 492504.
  • 4
    Y. Chen, Y. Huang, The full-discrete mixed finite element methods for nonlinear hyperbolic equations, Commun Nonlinear Sci Numer Simul 3 (3) (1998), 152155.
  • 5
    O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flows, Gordon and Breach, London, 1969.
  • 6
    I. Babuška, The finite element method with Lagrangian multipliers, Numer Math 20 (1973), 179192.
  • 7
    F. Brezzi, On the existence uniqueness and approximation of saddle point problems arising from Lagrangian multipliers, RAIRO Sèr Anal Numèr 8 (1974), 129151.
  • 8
    Z. Cai, R. Lazarov, T. A. Manteuffel, and S. F. MicCormick, First-order system least squares for second-order partial differential equations, II, SIAM J Numer Anal 34 (1997), 425454.
  • 9
    A. Pehlivanov, G. F. Carey, and D. Lazarov, Least-squares mixed finite elements for second-order elliptic problems, SIAM J Numer Anal 31 (1994), 13681377.
  • 10
    F. Moleiro, C. M. Mota Soares, C. A. Mota Soares, and J. N. Reddy, Layerwise mixed least-squares models for static and free vibration analysis of multilayered composite plates, Compos Struct 92 (2010), 23282338.
  • 11
    H. Rui, S. Kim, and S. D. Kim, A remark on least-squares mixed element methods for reaction-diffusion problems, J Comp Appl Math 202 (2007), 230236.
  • 12
    H. Guo, H. X. Rui, and C. Lin, Least-squares Galerkin procedure for second-order hyperbolic equations, J Syst Sci Complex 24(2) (2011), 381393.
  • 13
    H. Rui, S. D. Kim, and S. Kim, Split least-squares finite element methods for linear and nonlinear parabolic problems, J Comp Appl Math 223(2) (2008), 938952.
  • 14
    H. Guo, H. X. Rui, and C. Lin, A remark on least-squares Galerkin procedures for pseudo- hyperbolic equations, J Comput Appl Math 229(1) (2009), 108119.
  • 15
    Q. Lin and N. N. Yan, High efficiency FEM construction and analysis, Hebei University Press, Hebei, 1996.
  • 16
    Q. Lin and Q. D. Zhu, The preprocessing and postprocessing for the finite element method, Shanghai Sci. and Tech, Press, Shanghai, 1994.
  • 17
    Y. Chen and D. Yu, Superconvergence of least-squares mixed finite element for second-order elliptic problems, J Comput Math 21 (6) (2003), 825832.
  • 18
    Y. Chen and M. Zhang, Superconvergence of least-squares mixed finite element for symmetric elliptic problems, Appl Numer Math 48 (2004), 195204.
  • 19
    R. A. Adams, Sobolev spaces, Academic Press, New York, 1975.
  • 20
    P. A. Raviart and J. M. Thomas, A mixed finite element method for 2nd order elliptic problems. Mathematical Aspects of finite element methods Lecture Notes in Mathematics, 606, Springer, Berlin, 1977, pp. 292315.
  • 21
    F. Brezzi, J. Douglas, M. Fortin, and L. Marini, Efficient rectangular mixed finite elements in two and three spaces variables, RAIRO Modèl Math Anal Numèr 21 (1987), 581604.
  • 22
    C. M. Chen and Y. Q. Huang, High accuracy theory of finite elements, Hunan Science Press, Changsha, 1994.
  • 23
    L. B. Wahlbin, Superconvergence in Galerkin finite element methods (Lecture Notes in Mathematics) (1995).