Free access
Issue
ESAIM: M2AN
Volume 43, Number 2, March-April 2009
Page(s) 353 - 375
DOI http://dx.doi.org/10.1051/m2an:2008048
Published online 05 December 2008
  1. I. Babuška, M. Feistauer and P. Šolín, On one approach to a posteriori error estimates for evolution problems solved by the method-of-lines. Numer. Math. 89 (2001) 225–256. [CrossRef] [MathSciNet]
  2. R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2001) 1–102. [CrossRef] [MathSciNet]
  3. A. Bergam, C. Bernardi and Z. Mghazli, A posteriori analysis of the finite element discretization of some parabolic equations. Math. Comp. 74 (2005) 1117–1138. [CrossRef] [MathSciNet]
  4. M.A. Biot, General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1941) 155–169. [CrossRef]
  5. C. Chavant and A. Millard, Simulation d'excavation en comportement hydro-mécanique fragile. Technical report, EDF R&D/AMA and CEA/DEN/SEMT (2007) http://www.gdrmomas.org/ex_qualifications.html.
  6. Z. Chen and J. Feng, An adaptive finite element algorithm with reliable and efficient error control for linear parabolic problems. Math. Comp. 73 (2004) 1167–1193. [CrossRef] [MathSciNet]
  7. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77–84.
  8. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. I. A linear model problem. SIAM J. Numer. Anal. 28 (1991) 43–77.
  9. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. II. Optimal error estimates in ƖƖ2 and ƖƖ. SIAM J. Numer. Anal. 32 (1995) 706–740.
  10. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements, Applied Mathematical Sciences 159. Springer-Verlag, New York (2004).
  11. O. Lakkis and Ch. Makridakis, Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems. Math. Comp. 75 (2006) 1627–1658. [CrossRef] [MathSciNet]
  12. Ch. Makridakis and R.H. Nochetto, Ellitpic reconstruction and a posteriori error estimates for elliptic problems. SIAM J. Numer. Anal. 41 (2003) 1585–1594. [CrossRef] [MathSciNet]
  13. S. Meunier, Analyse d'erreur a posteriori pour les couplages hydro-mécaniques et mise en œuvre dans Code_Aster. Ph.D. Thesis, École nationale des ponts et chaussées, France (2007).
  14. M.A. Murad and A.F.D. Loula, Improved accuracy in finite element analysis of Biot's consolidation problem. Comput. Meth. Appl. Mech. Engrg. 95 (1992) 359–382. [CrossRef]
  15. M.A. Murad and A.F.D. Loula, On stability and convergence of finite element approximations of Biot's consolidation problem. Internat. J. Numer. Methods Engrg. 37 (1994) 645–667. [CrossRef] [MathSciNet]
  16. M.A. Murad, V. Thomée and A.F.D. Loula, Asymptotic behavior of semidiscrete finite-element approximations of Biot's consolidation problem. SIAM J. Numer. Anal. 33 (1996) 1065–1083. [CrossRef] [MathSciNet]
  17. M. Picasso, Adaptive finite elements for a linear parabolic problem. Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237. [CrossRef] [MathSciNet]
  18. R.L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet]
  19. R.E. Showalter, Diffusion in deformable media. IMA Volumes in Mathematics and its Applications 131 (2000) 115–130.
  20. R.E. Showalter, Diffusion in poro-elastic media. J. Math. Anal. Appl. 251 (2000) 310–340. [CrossRef] [MathSciNet]
  21. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems. Springer-Verlag, Berlin (1997).
  22. R. Verfürth, A posteriori error estimations and adaptative mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67–83. [CrossRef] [MathSciNet]
  23. R. Verfürth, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley, Chichester, UK (1996).
  24. R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation. Calcolo 40 (2003) 195–212. [CrossRef] [MathSciNet]
  25. K. von Terzaghi, Theoretical Soil Mechanics. Wiley, New York (1936).
  26. M. Wheeler, A priori L2 error estimates for Galerkin approximations to parabolic partial differential equations. SIAM J. Numer. Anal. 10 (1973) 723–759. [CrossRef] [MathSciNet]

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