Free access
Issue
ESAIM: M2AN
Volume 44, Number 3, May-June 2010
Page(s) 455 - 484
DOI http://dx.doi.org/10.1051/m2an/2010009
Published online 04 February 2010
  1. I. Babuška and W.C. Rheinboldt, Error estimates for adaptive finite element method. SIAM J. Numer. Anal. 15 (1978) 736–754. [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.
  3. A. Bergam, C. Bernardi and Z. Mghazli, A posteriori analysis of the finite element discretization of some parabolic equations. Math. Comp. 74 (2004) 1117–1138. [CrossRef] [MathSciNet]
  4. C. Bernardi and R. Verfürth, Adaptive finite element methods for elliptic equations with non-smooth coefficients. Numer. Math. 85 (2000) 579–608. [CrossRef] [MathSciNet]
  5. S. Berrone, Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients. ESAIM: M2AM 40 (2006) 991–1021. [CrossRef]
  6. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam (1978).
  7. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77–84.
  8. W. Dörfler, A convergent adaptive algorithm for Poisson's equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [CrossRef] [MathSciNet]
  9. M. Dryja, M.V. Sarkis and O.B. Widlund, Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer. Math. 72 (1996) 313–348. [CrossRef] [MathSciNet]
  10. K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems. V. Long-time integration. SIAM J. Numer. Anal. 32 (1995) 1750–1763. [CrossRef] [MathSciNet]
  11. K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations. Acta Numer. 4 (1995) 105–158. [CrossRef]
  12. B.S. Kirk, J.W. Peterson, R. Stogner and S. Petersen, LibMesh. The University of Texas, Austin, CFDLab and Technische Universität Hamburg, Hamburg, http://libmesh.sourceforge.net.
  13. B.P. Lamichhane and B.I. Wohlmuth, Higher order dual Lagrange multiplier spaces for mortar finite element discretizations. Calcolo 39 (2002) 219–237. [CrossRef] [MathSciNet]
  14. B.P. Lamichhane, R.P. Stevenson and B.I. Wohlmuth, Higher order mortar finite element methods in 3D with dual Lagrange multiplier bases. Numer. Math. 102 (2005) 93–121. [CrossRef] [MathSciNet]
  15. P. Morin, R.H. Nochetto and K.G. Siebert, Convergence of adaptive finite element methods. SIAM Rev. 44 (2002) 631–658. [CrossRef] [MathSciNet]
  16. M. Petzoldt, A posteriori error estimators for elliptic equations with discontinuous coefficients. Adv. Comput. Math. 16 (2002) 47–75. [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. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [CrossRef] [MathSciNet]
  19. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. John Wiley & Sons, Chichester-New York (1996).
  20. R. Verfürth, A posteriori error estimates for finite element discretization of the heat equations. Calcolo 40 (2003) 195–212. [CrossRef] [MathSciNet]
  21. B.I. Wohlmuth, A mortar finite element method using dual spaces for the Lagrange multiplier. SIAM J. Numer. Anal. 38 (2000) 989–1012. [CrossRef] [MathSciNet]
  22. O.C. Zienkiewicz and J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis. Internat. J. Numer. Methods Engrg. 24 (1987) 337–357. [CrossRef] [MathSciNet]

Recommended for you