Free Access
Volume 53, Number 6, November-December 2019
Page(s) 2121 - 2159
Published online 12 December 2019
  1. R.A. Adams and J.J. Fournier, Sobolev spaces. In: Vol. 140 of Pure and Applied Mathematics. Academic Press, New York, London (2003). [Google Scholar]
  2. A. Alonso, Error estimators for a mixed method. Numer. Math. 74 (1996) 385–395. [Google Scholar]
  3. I. Babuška and W.C. Rheinboldt, Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978) 736–754. [Google Scholar]
  4. C. Bernardi and V. Girault, A local regularisation operation for triangular and quadrilateral finite elements. SIAM J. Numer. Anal. 35 (1998) 1893–1916. [Google Scholar]
  5. C. Bernardi, F. Hecht and R. Verfürth, A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions. ESAIM: M2AN 43 (2009) 185–1201. [CrossRef] [EDP Sciences] [Google Scholar]
  6. C. Bernardi, J. Dakroub, G. Mansour and T. Sayah, A posteriori analysis of iterative algorithms for Navier-Stokes problem. ESAIM: M2AN 50 (2016) 1035–1055. [CrossRef] [EDP Sciences] [Google Scholar]
  7. C. Bernardi, S. Dib, V. Girault, F. Hecht, F. Murat and T. Sayah, Finite element methods for Darcy’s problem coupled with the heat equation. Numer. Math. 139 (2018) 315–348. [Google Scholar]
  8. D. Braess and R. Verfürth, A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431–2444. [Google Scholar]
  9. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, NY 15 (1991). [CrossRef] [Google Scholar]
  10. C. Carstensen, A posteriori error estimate for the mixed finite element method. Math. Comput. 66 (1997) 465–476. [Google Scholar]
  11. W. Chen and Y. Wang, A posteriori estimate for the # conforming mixed finite element for the coupled Darcy-Stokes system. J. Comput. Appl. Math. 255 (2014) 502–516. [Google Scholar]
  12. P.G. Ciarlet, Basic error estimates for elliptic problems. In: Vol. II of Handbook of Numerical Analysis. North-Holland, Amsterdam (1991) 17–351. [Google Scholar]
  13. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77–84. [Google Scholar]
  14. E. Colmenares, G.N. Gatica and R.Y. Oyarzua, A posteriori error analysis of an augmented mixed-primal formulation for the stationary boussinesq model. Calcolo 54 (2017) 1055–1095. [CrossRef] [Google Scholar]
  15. E. Colmenares, G.N. Gatica and R.Y. Oyarzua, A posteriori error analysis of an augmented fully-mixed formulation for the stationary boussinesq model. Comput. Math. App. 77 (2019) 693–714. [Google Scholar]
  16. A. El Akkad, A. El Khalfi and N. Guessous, An a posteriori estimate for mixed finite element approximations of the Navier-Stokes equations. J. Korean Math. Soc. 48 (2011) 529–550. [CrossRef] [MathSciNet] [Google Scholar]
  17. V. Ervin, W. Layton and J. Maubach, A posteriori error estimators for a two-level finite element method for the Navier-Stokes equations. I.C.M.A. Tech. Report, Univ. of Pittsburgh (1995). [Google Scholar]
  18. G.N. Gatica, R. Ruiz-Baier and G. Tierra, A mixed finite element method for Darcy’s equations with pressure dependent porosity. Math. Comput. 85 (2016) 1–33. [Google Scholar]
  19. V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations. In: Vol. 5of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1986) Theory and algorithms. [CrossRef] [Google Scholar]
  20. F. Hecht, New development in FreeFem++. J. Numer. Math. 20 (2012) 251–266. [CrossRef] [MathSciNet] [Google Scholar]
  21. H. Jin and S. Prudhomme, A posteriori error estimation in finite element analysis. Comput. Methods Appl. Mech. Eng. 159 (1998) 19–48. [Google Scholar]
  22. V. John, Residual a posteriori error estimates for two-level finite element methods for the Navier-Stokes equations. Appl. Numer. Math. 37 (2001) 503–518. [Google Scholar]
  23. C. Lovadina and R. Stenberg, Energy norm a posteriori error estimates for mixed finite element methods. Math. Comput. 75 (2006) 1659–1674. [Google Scholar]
  24. J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). [Google Scholar]
  25. P.-A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems (rome, 1975). In: Mathematical Aspects of Finite Element Methods. Springer, Berlin (1977) 292–315. [CrossRef] [Google Scholar]
  26. J.E. Roberts and J.-M. Thomas, Mixed and hybrid methods. In Vol II of Handbook of Numerical Analysis, Finite Element Methods (Part I). North-Holland, Amsterdam (1991) 523–637. [CrossRef] [Google Scholar]
  27. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  28. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Mathematics. Wiley and Teubner, New York, NY (1996). [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