Free Access
Issue
ESAIM: M2AN
Volume 47, Number 3, May-June 2013
Page(s) 789 - 805
DOI https://doi.org/10.1051/m2an/2012050
Published online 29 March 2013
  1. D.N. Arnold, F. Brezzi and J. Douglas, Jr., PEERS: a new mixed finite element for plane elasticity. Japan J. Appl. Math. 1 (1984) 347–367. [CrossRef] [MathSciNet] [Google Scholar]
  2. D.N. Arnold, J. Douglas, Jr. and C.P. Gupta, A family of higher order mixed finite element methods for plane elasticity. Numer. Math. 45 (1984) 1–22. [CrossRef] [MathSciNet] [Google Scholar]
  3. D.N. Arnold, R.S. Falk and R. Winther, Mixed finite element methods for linear elasticity with weakly imposed symmetry. Math. Comput. 76 (2007) 1699–1723 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Barlow, Optimal stress location in finite element method. Internat. J. Numer. Methods Engrg. 10 (1976) 243–251. [CrossRef] [Google Scholar]
  5. D. Boffi, F. Brezzi, L.F. Demkowicz, R.G. Durán, R.S. Falk and M. Fortin, Mixed finite elements, compatibility conditions, and applications, Springer-Verlag, Berlin. Lect. Notes Math. 1939 (2008). Lectures given at the C.I.M.E. Summer School held in Cetraro, June 26–July 1, 2006, edited by Boffi and Lucia Gastaldi. [Google Scholar]
  6. D. Boffi, F. Brezzi and M. Fortin, Reduced symmetry elements in linear elasticity. Commun. Pure Appl. Anal. 8 (2009) 95–121. [MathSciNet] [Google Scholar]
  7. F. Brezzi, J. Douglas, Jr. and L.D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47 (1985) 217–235. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer Series in Comput. Math. Springer-Verlag, New York 15 (1991). [Google Scholar]
  9. F. Brezzi, J. Rappaz and P.-A. Raviart, Finite-dimensional approximation of nonlinear problems. I. Branches of nonsingular solutions. Numer. Math. 36 (1980/81) 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  10. Z. Cai, C. Wang and S. Zhang, Mixed finite element methods for incompressible flow: stationary Navier-Stokes equations. SIAM J. Numer. Anal. 48 (2010) 79–94. [CrossRef] [MathSciNet] [Google Scholar]
  11. Z. Cai and Y. Wang, Pseudostress-velocity formulation for incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 63 (2010) 341–356. [CrossRef] [Google Scholar]
  12. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77–84. [Google Scholar]
  13. B. Cockburn, J. Gopalakrishnan and J. Guzmán, A new elasticity element made for enforcing weak stress symmetry. Math. Comput. 79 (2010) 1331–1349. [CrossRef] [Google Scholar]
  14. M. Farhloul and H. Manouzi, Analysis of non-singular solutions of a mixed Navier-Stokes formulation. Comput. Methods Appl. Mech. Engrg. 129 (1996) 115–131. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Farhloul, S. Nicaise and L. Paquet, A refined mixed finite-element method for the stationary Navier-Stokes equations with mixed boundary conditions. IMA J. Numer. Anal. 28 (2008) 25–45. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Farhloul, S. Nicaise and L. Paquet, A priori and a posteriori error estimations for the dual mixed finite element method of the Navier-Stokes problem. Numer. Methods Partial Differ. Equ. 25 (2009) 843–869. [CrossRef] [Google Scholar]
  17. V. Girault and P.A. Raviart, Finite Element Approximation of the Navier Stokes Equations. Springer Verlag, Berlin, Heidelbert, New York. Lect. Notes Math. 749 (1979). [Google Scholar]
  18. J. Gopalakrishnan and J. Guzmán, A second elasticity element using the matrix bubble, IMA J. Numer. Anal. 32 (2012) 352–372. [CrossRef] [MathSciNet] [Google Scholar]
  19. J.S. Howell and N.J. Walkington, Inf-sup conditions for twofold saddle point problems. Numer. Math. 118 (2011) 663–693. [CrossRef] [MathSciNet] [Google Scholar]
  20. W. Layton, Introduction to the numerical analysis of incompressible viscous flows, Computational Science & Engineering, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA 6 (2008). [Google Scholar]
  21. P.-A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in Mathematical aspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome, 1975), Springer, Berlin. Lect. Notes Math. 606 (1977) 292–315. [Google Scholar]
  22. L.R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. RAIRO Modél. Math. Anal. Numér. 19 (1985) 111–143. [MathSciNet] [Google Scholar]
  23. A. Shapiro, The use of an exact solution of the navier-stokes equations in a validation test of a three-dimensional non-hydrostatic numerical model. Mon. Wea. Rev. 121 (1993) 2420–2425. [CrossRef] [Google Scholar]
  24. R.E. Showalter, Monotone operators in Banach space and nonlinear partial differential equations, Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI 49 (1997). [Google Scholar]
  25. R. Stenberg, Analysis of mixed finite elements methods for the Stokes problem: a unified approach. Math. Comput. 42 (1984) 9–23. [Google Scholar]
  26. R. Stenberg, A family of mixed finite elements for the elasticity problem. Numer. Math. 53 (1988) 513–538. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Temam, Navier-Stokes Equations, North Holland (1977). [Google Scholar]
  28. S. Zhang, A new family of stable mixed finite elements for the 3D Stokes equations. Math. Comput. 74 (2005) 543–554. [CrossRef] [Google Scholar]
  29. Z. Zhang, Ultraconvergence of the patch recovery technique. Math. Comput. 65 (1996) 1431–1437. [CrossRef] [Google Scholar]
  30. O.C. Zienkiewicz, R. Taylor and J. Too, Reduced integration technique in general analysis of plates and shells. Inter. J. Numer. Methods Engrg. 3 (1971) 275–290. [CrossRef] [Google Scholar]
  31. O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates I. The recovery technique. Internat. J. Numer. Methods Engrg. 33 (1992) 1331–1364. [CrossRef] [MathSciNet] [Google Scholar]
  32. O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates. II. Error estimates and adaptivity. Inter. J. Numer. Methods Engrg. 33 (1992) 1365–1382. [CrossRef] [Google Scholar]
  33. O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput. Methods Appl. Mech. Engrg. 101 (1992) 207–224. Reliability in computational mechanics (Kraków 1991). [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you