Free Access
Issue |
ESAIM: M2AN
Volume 43, Number 2, March-April 2009
|
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Page(s) | 353 - 375 | |
DOI | https://doi.org/10.1051/m2an:2008048 | |
Published online | 05 December 2008 |
- 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]
- 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]
- 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]
- M.A. Biot, General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1941) 155–169. [CrossRef] [Google Scholar]
- 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]
- 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]
- P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77–84. [Google Scholar]
- 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]
- K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. II. Optimal error estimates in Ɩ∞Ɩ2 and Ɩ∞Ɩ∞. SIAM J. Numer. Anal. 32 (1995) 706–740. [Google Scholar]
- A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements, Applied Mathematical Sciences 159. Springer-Verlag, New York (2004). [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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. [Google Scholar]
- 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]
- M. Picasso, Adaptive finite elements for a linear parabolic problem. Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237. [Google Scholar]
- R.L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [Google Scholar]
- R.E. Showalter, Diffusion in deformable media. IMA Volumes in Mathematics and its Applications 131 (2000) 115–130. [Google Scholar]
- R.E. Showalter, Diffusion in poro-elastic media. J. Math. Anal. Appl. 251 (2000) 310–340. [CrossRef] [MathSciNet] [Google Scholar]
- V. Thomée, Galerkin Finite Element Methods for Parabolic Problems. Springer-Verlag, Berlin (1997). [Google Scholar]
- R. Verfürth, A posteriori error estimations and adaptative mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67–83. [CrossRef] [MathSciNet] [Google Scholar]
- R. Verfürth, A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley, Chichester, UK (1996). [Google Scholar]
- R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation. Calcolo 40 (2003) 195–212. [CrossRef] [MathSciNet] [Google Scholar]
- K. von Terzaghi, Theoretical Soil Mechanics. Wiley, New York (1936). [Google Scholar]
- 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]
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