Free Access
Volume 47, Number 6, November-December 2013
Page(s) 1797 - 1820
Published online 07 October 2013
  1. Y. Achdou, C. Bernardi and F. Coquel, A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. Numer. Math. 96 (2003) 17–42. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Azaïez, F. Ben Belgacem and C. Bernardi, The mortar spectral element method in domains of operators, Part I: The divergence operator and Darcy’s equations. IMA J. Numer. Anal. 26 (2006) 131–154. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Azaïez, F. Ben Belgacem, C. Bernardi and N. Chorfi, Spectral discretization of Darcy’s equations with pressure dependent porosity. Appl. Math. Comput. 217 (2010) 1838–1856. [CrossRef] [Google Scholar]
  4. M. Azaïez, F. Ben Belgacem, M. Grundmann and H. Khallouf, Staggered grids hybrid-dual spectral element method for second-order elliptic problems, Application to high-order time splitting methods for Navier–Stokes equations. Comput. Methods Appl. Mech. Engrg. 166 (1998) 183–199. [CrossRef] [MathSciNet] [Google Scholar]
  5. C. Bernardi, Indicateurs d’erreur en hN version des éléments spectraux. Modél. Math. et Anal. Numér. 30 (1996) 1–38. [Google Scholar]
  6. C. Bernardi, A. Blouza, N. Chorfi and N. Kharrat, A penalty algorithm for the spectral element discretization of the Stokes problem. Math. Model. Numer. Anal. 45 (2011) 201–216. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  7. C. Bernardi, T. Chacón Rebollo, F. Hecht and R. Lewandowski, Automatic insertion of a turbulence model in the finite element discretization of the Navier–Stokes equations. Math. Models Methods Appl. Sci. 19 (2009) 1139–1183. [CrossRef] [Google Scholar]
  8. C. Bernardi, F. Coquel and P.-A. Raviart, Automatic coupling and finite element discretization of the Navier–Stokes and heat equations, Internal Report R10001, Labotatoire Jacques-Louis Lions, Paris (2010). [Google Scholar]
  9. C. Bernardi, M. Dauge and Y. Maday, Polynomials in Sobolev Spaces and Application to the Mortar Spectral Element Method, in preparation. [Google Scholar]
  10. C. Bernardi and Y. Maday, Spectral Methods, in the Handbook of Numerical Analysis V, edited by P.G. Ciarlet and J.-L. Lions. North-Holland (1997) 209–485. [Google Scholar]
  11. C. Bernardi, Y. Maday and F. Rapetti, Discrétisations variationnelles de problèmes aux limites elliptiques, Collection Mathématiques et Applications vol. 45. Springer-Verlag (2004). [Google Scholar]
  12. M. Braack and A. Ern, A posteriori control of modeling errors and discretization errors. Multiscale Model. Simul. 1 (2003) 221–238. [CrossRef] [Google Scholar]
  13. H. Brezis and P. Mironescu, Gagliardo–Nirenberg, composition and products in fractional Sobolev spaces, J. Evol. Equ. 1 (2001), 387–404. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Brezzi, J. Rappaz and P.-A. Raviart, Finite dimensional approximation of nonlinear problems, Part I: Branches of nonsingular solutions. Numer. Math. 36 (1980) 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  15. T. Chacón Rebollo, S. Del Pino and D. Yakoubi, An iterative procedure to solve a coupled two-fluids turbulence model. Math. Model. Numer. Anal. 44 (2010) 693–713. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  16. A.L. Chaillou and M. Suri, Computable error estimators for the approximation of nonlinear problems by linearized models. Comput. Methods Appl. Mech. Engrg. 196 (2006) 210–224. [Google Scholar]
  17. M. Daadaa, Discrétisation spectrale et par éléments spectraux des équations de Darcy, Ph.D. Thesis, Université Pierre et Marie Curie, Paris (2009). [Google Scholar]
  18. M. Dauge, Neumann and mixed problems on curvilinear polyhedra. Integr. Equ. Oper. Th. 15 (1992) 227–261. [Google Scholar]
  19. L. El Alaoui, A. Ern and M. Vohralík, Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems. Comput. Methods Appl. Mech. Engrg. 200 (2011) 2782–2795. [Google Scholar]
  20. V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations, Theory and Algorithms. Springer–Verlag (1986). [Google Scholar]
  21. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. I. Dunod, Paris (1968). [Google Scholar]
  22. N.G. Meyers, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Sc. Norm. Sup. Pisa 17 (1963) 189–206. [Google Scholar]
  23. J. Pousin and J. Rappaz, Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems. Numer. Math. 69 (1994) 213–231. [CrossRef] [MathSciNet] [Google Scholar]
  24. K.R. Rajagopal, On a hierarchy of approximate models for flows of incompressible fluids through porous solid. Math. Models Methods Appl. Sci. 17 (2007) 215–252. [CrossRef] [MathSciNet] [Google Scholar]
  25. G. Talenti, Best constant in Sobolev inequality. Ann. Math. Pura ed Appl. Serie IV 110 (1976) 353–372. [Google Scholar]
  26. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley ans Teubner (1996). [Google Scholar]

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