Free Access
Issue |
ESAIM: M2AN
Volume 37, Number 6, November-December 2003
|
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Page(s) | 1013 - 1043 | |
DOI | https://doi.org/10.1051/m2an:2003065 | |
Published online | 15 November 2003 |
- M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis. Wiley (2000). [Google Scholar]
- Th. Apel, Anisotropic finite elements: Local estimates and applications, Advances in Numerical Mathematics. Teubner, Stuttgart (1999). [Google Scholar]
- I. Babuška, T. Strouboulis and C.S. Upadhyay, A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles. Comput. Methods Appl. Mech. Engrg. 114 (1994) 307–378. [CrossRef] [MathSciNet] [Google Scholar]
- I. Babuška, T. Strouboulis, C.S. Upadhyay, S.K. Gangaraj and K. Copps, Validation of a posteriori error estimators by numerical approach. Int. J. Numer. Methods Eng. 37 (1994) 1073–1123. [CrossRef] [Google Scholar]
- S. Bartels and C. Carstensen, Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: High order FEM. Math. Comp. 71 (2002) 971–994. [CrossRef] [MathSciNet] [Google Scholar]
-
J.H. Bramble, J.E. Pasciak and O. Steinbach, On the stability of the L2-projection in
. Math. Comp. 71 (2002) 147–156. [Google Scholar]
- C. Carstensen, Merging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for H1-stability of the L2-projection onto finite element spaces. Math. Comp. 71 (2002) 157–163. [CrossRef] [MathSciNet] [Google Scholar]
- C. Carstensen and S. Bartels, Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM. Math. Comp. 71 (2002) 945–969. [CrossRef] [MathSciNet] [Google Scholar]
- P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1978). [Google Scholar]
- M. Dobrowolski, S. Gräf and C. Pflaum, On a posteriori error estimators in the finite element method on anisotropic meshes. Electron. Trans. Numer. Anal. 8 (1999) 36–45. [MathSciNet] [Google Scholar]
- G. Kunert, A posteriori error estimation for anisotropic tetrahedral and triangular finite element meshes. Logos Verlag, Berlin (1999). Also Ph.D. thesis, TU Chemnitz, http://archiv.tu-chemnitz.de/pub/1999/0012/index.html [Google Scholar]
- G. Kunert, An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes. Numer. Math. 86 (2000) 471–490, DOI 10.1007/s002110000170. [CrossRef] [MathSciNet] [Google Scholar]
- G. Kunert, A local problem error estimator for anisotropic tetrahedral f inite element meshes. SIAM J. Numer. Anal. 39 (2001) 668–689. [CrossRef] [MathSciNet] [Google Scholar]
- G. Kunert, A posteriori L2 error estimation on anisotropic tetrahedral finite element meshes. IMA J. Numer. Anal. 21 (2001) 503–523. [CrossRef] [MathSciNet] [Google Scholar]
- 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]
- G. Kunert and S. Nicaise, Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes, preprint SFB393/01–20, TU Chemnitz, July 2001. Also http://archiv.tu-chemnitz.de/pub/2001/0059/index.html [Google Scholar]
- 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, DOI 10.1007/s002110000152. [CrossRef] [MathSciNet] [Google Scholar]
- L.A. Oganesyan and L.A. Rukhovets, Variational-difference methods for the solution of elliptic equations. Izd. Akad. Nauk Armyanskoi SSR, Jerevan (1979), in Russian. [Google Scholar]
- G. Raugel, Résolution numérique par une méthode d'éléments finis du problème de Dirichlet pour le Laplacien dans un polygone. C. R. Acad. Sci. Paris, Sér. I Math 286 (1978) A791–A794. [Google Scholar]
- R. Rodriguez, Some remarks on the Zienkiewicz–Zhu estimator. Numer. Meth. PDE 10 (1994) 625–635. [CrossRef] [Google Scholar]
- H.G. Roos and T. Linß, Gradient recovery for singularly perturbed boundary value problems II: Two-dimensional convection-diffusion. Math. Models Methods Appl. Sci. 11 (2001) 1169–1179. [CrossRef] [MathSciNet] [Google Scholar]
- K.G. Siebert, An a posteriori error estimator for anisotropic refinement. Numer. Math. 73 (1996) 373–398. [CrossRef] [MathSciNet] [Google Scholar]
- O. Steinbach, On the stability of the L2-projection in fractional Sobolev spaces. Numer. Math. 88 (2001) 367–379. [CrossRef] [MathSciNet] [Google Scholar]
- R. Verfürth, A review of a posteriori error estimation and adaptive mesh–refinement techniques. Wiley-Teubner, Chichester, Stuttgart (1996). [Google Scholar]
- Zh. Zhang, Superconvergent finite element method on a Shishkin mesh for convection-diffusion problems. Report 98-006, Texas Tech University (1998). [Google Scholar]
- 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. [Google Scholar]
- O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput. Methods Appl. Mech. Engrg. 101 (1992) 207–224. [CrossRef] [MathSciNet] [Google Scholar]
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