Free Access
Issue
ESAIM: M2AN
Volume 43, Number 2, March-April 2009
Page(s) 353 - 375
DOI https://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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  4. M.A. Biot, General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1941) 155–169. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  7. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77–84. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  10. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements, Applied Mathematical Sciences 159. Springer-Verlag, New York (2004). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  17. M. Picasso, Adaptive finite elements for a linear parabolic problem. Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237. [CrossRef] [MathSciNet] [Google Scholar]
  18. R.L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  19. R.E. Showalter, Diffusion in deformable media. IMA Volumes in Mathematics and its Applications 131 (2000) 115–130. [Google Scholar]
  20. R.E. Showalter, Diffusion in poro-elastic media. J. Math. Anal. Appl. 251 (2000) 310–340. [CrossRef] [MathSciNet] [Google Scholar]
  21. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems. Springer-Verlag, Berlin (1997). [Google Scholar]
  22. R. Verfürth, A posteriori error estimations and adaptative mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67–83. [CrossRef] [MathSciNet] [Google Scholar]
  23. R. Verfürth, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley, Chichester, UK (1996). [Google Scholar]
  24. R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation. Calcolo 40 (2003) 195–212. [CrossRef] [MathSciNet] [Google Scholar]
  25. K. von Terzaghi, Theoretical Soil Mechanics. Wiley, New York (1936). [Google Scholar]
  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] [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