Free Access
Volume 40, Number 2, March-April 2006
Page(s) 239 - 267
Published online 21 June 2006
  1. M. Ainsworth and I. Babuška, Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. SIAM J. Numer. Anal. 36 (1999) 331–353 (electronic). See also Corrigendum at [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Ainsworth and J.T. Oden, A unified approach to a posteriori error estimation using element residual methods. Numer. Math. 65 (1993) 23–50. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Ainsworth and J.T. Oden, A Posteriori Error Estimation in Finite Element Analysis. Wiley (2000). [Google Scholar]
  4. T. Apel, Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements. Computing 60 (1998) 157–174. [CrossRef] [MathSciNet] [Google Scholar]
  5. T. Apel, Treatment of boundary layers with anisotropic finite elements. Z. Angew. Math. Mech. (1998). [Google Scholar]
  6. T. Apel, Anisotropic finite elements: local estimates and applications. B.G. Teubner, Stuttgart (1999). [Google Scholar]
  7. T. Apel, S. Grosman, P.K. Jimack and A. Meyer, A new methodology for anisotropic mesh refinement based upon error gradients. Appl. Numer. Math. 50 (2004) 329–341. [CrossRef] [MathSciNet] [Google Scholar]
  8. T. Apel and G. Lube, Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem. Appl. Numer. Math. 26 (1998) 415–433. [CrossRef] [MathSciNet] [Google Scholar]
  9. I. Babuška and W. Rheinboldt, A posteriori error estimates for the finite element method. Int. J. Numer. Meth. Eng. 12 (1978) 1597–1615. [CrossRef] [Google Scholar]
  10. R. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations. Math. Comp. 44 (1985) 283–301. [CrossRef] [MathSciNet] [Google Scholar]
  11. H. Bufler and E. Stein, Zur Plattenberechnung mittels finiter Elemente. Ingenier Archiv 39 (1970) 248–260. [CrossRef] [Google Scholar]
  12. P.G. Ciarlet, The finite element method for elliptic problems. North-Holland Publishing Co., Amsterdam. Studies in Mathematics and its Applications, Vol. 4, (1978). [Google Scholar]
  13. M. Dobrowolski, S. Gräf and C. Pflaum, On a posteriori error estimators in the infinte element method on anisotropic meshes. Electron. Trans. Numer. Anal. 8 (1999) 36–45. [Google Scholar]
  14. S. Grosman, The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshes. SFB393-Preprint 2, Technische Universität Chemnitz, SFB 393 (Germany), (2004). [Google Scholar]
  15. R. Hagen, S. Roch, and B. Silbermann, C*-algebras and numerical analysis. Marcel Dekker Inc., New York (2001). [Google Scholar]
  16. H. Han and R.B. Kellogg, Differentiability properties of solutions of the equation Formula in a square. SIAM J. Math. Anal. 21 (1990) 394–408. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Kunert, A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes. Logos Verlag, Berlin, 1999. Also PhD thesis, TU Chemnitz, [Google Scholar]
  18. G. Kunert, An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer. Math. 86 (2000) 471–490. [CrossRef] [MathSciNet] [Google Scholar]
  19. G. Kunert, A local problem error estimator for anisotropic tetrahedral finite element meshes. SIAM J. Numer. Anal. 39 (2001) 668–689. [CrossRef] [MathSciNet] [Google Scholar]
  20. G. Kunert, Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes. Adv. Comput. Math. 15 (2001) 237–259. [CrossRef] [MathSciNet] [Google Scholar]
  21. G. Kunert, Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes. ESAIM: M2AN 35 (2001) 1079–1109. [CrossRef] [EDP Sciences] [Google Scholar]
  22. G. Kunert and R. Verfürth, Edge residuals dominate a posteriori error estimates for linear finite element methods on anisotropic triangular and tetrahedral meshes. Numer. Math. 86 (2000) 283–303. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Ladevèze and D. Leguillon, Error estimate procedure in the finite element method and applications. SIAM J. Numer. Anal. 20 (1983) 485–509. [CrossRef] [MathSciNet] [Google Scholar]
  24. K.G. Siebert, An a posteriori error estimator for anisotropic refinement. Numer. Math. 73 (1996) 373–398. [CrossRef] [MathSciNet] [Google Scholar]
  25. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley-Teubner Series Advances in Numerical Mathematics. Chichester: John Wiley & Sons. Stuttgart: B.G. Teubner (1996). [Google Scholar]
  26. M. Vogelius and I. Babuška, On a dimensional reduction method. I. The optimal selection of basis functions. Math. Comp. 37 (1981) 31–46. [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