Quasi-interpolation and a posteriori error analysis in finite element methods

Carsten Carstensen

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 6, page 1187-1202
  • ISSN: 0764-583X

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Carstensen, Carsten. "Quasi-interpolation and a posteriori error analysis in finite element methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.6 (1999): 1187-1202. <http://eudml.org/doc/193967>.

@article{Carstensen1999,
author = {Carstensen, Carsten},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {quasi-interpolation; a posteriori error analysis; finite element method; elliptic model problem},
language = {eng},
number = {6},
pages = {1187-1202},
publisher = {Dunod},
title = {Quasi-interpolation and a posteriori error analysis in finite element methods},
url = {http://eudml.org/doc/193967},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Carstensen, Carsten
TI - Quasi-interpolation and a posteriori error analysis in finite element methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 6
SP - 1187
EP - 1202
LA - eng
KW - quasi-interpolation; a posteriori error analysis; finite element method; elliptic model problem
UR - http://eudml.org/doc/193967
ER -

References

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  1. [1] A. Alonso, Error estimators for a mixed method. Numer. Math. 74 (1996) 385-395. Zbl0866.65068MR1414415
  2. [2] I. Babu&#0161;ka and W.C. Rheinboldt, Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978). Zbl0398.65069MR483395
  3. [3] R. Becker and R. Rannacher, A feed-back approach to error control in finite element methods: basic analysis and examples. East-West J. Numer. Math. 4 (1996) 237-264. Zbl0868.65076MR1430239
  4. [4] D. Braess, Finite Eléments. Cambridge University Press (1997). Zbl0894.65054MR1463151
  5. [5] D. Braess and R. Verfürth, A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431-2444. Zbl0866.65071MR1427472
  6. [6] S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Texts Appl. Math. 15, Springer, New-York (1994). Zbl0804.65101MR1278258
  7. [7] F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag (1991). Zbl0788.73002MR1115205
  8. [8] C. Carstensen, A posteriori error estimate for themixed finite element method. Math. Comp. 66 (1997) 465-476. Zbl0864.65068MR1408371
  9. [9] C. Carstensen and S.A. Funken, Constants in Clément-interpolation error and residual based a posteriori error estimates in Finite Element Methods. Berichtsreihe des Mathematischen Seminars Kiel, Technical report 97-11, Christian-Albrechts-Universitât zu Kiel, Kiel (1997). Zbl0973.65091
  10. [10] C. Carstensen and S.A. Funken, Fully reliable localised error control in the FEM. Berichtsreihe des Mathematischen Seminars Kiel, Technical report 97-12, Christian-Albrechts-Universität zu Kiel, Kiel (1997). Zbl0956.65099
  11. [11] C. Carstensen and R. Verfürth, Edge residuals dominate a posteriori error estimates for low order finite element methods. Berichtsreihe des Mathematischen Seminars Kiel, Technical report 97-6, Christian-Albrechts-Universität zu Kiel; SIAM J.Numer. Anal. (to be published). Zbl0938.65124
  12. [12] P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. Zbl0368.65008MR400739
  13. [13] P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1978). Zbl0383.65058MR520174
  14. [14] E. Dari, R. Duran, C. Padra and V. Vampa, A posteriori error estimators for nonconforming finite element methods. Math.Modelling Numer. Anal. 30 (1996) 385-400. Zbl0853.65110MR1399496
  15. [15] K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations. Acta Numer.4 (1995) 105-158. Zbl0829.65122MR1352472
  16. [16] V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer, Berlin (1986). Zbl0585.65077MR851383
  17. [17] R.H.W. Hoppe and B. Wohlmuth, Element-orientated and edge-orientated local error estimates for nonconforming finite element methods. Math. Modelling Numer. Anal. 30 (1996) 237-263. Zbl0843.65075MR1382112
  18. [18] R. Temam, Theory and Numerical Analysis of the Navier-Stokes Equations. North-Holland (1977). Zbl0383.35057MR769654
  19. [19] R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley-Teubner (1996). Zbl0853.65108
  20. [20] B. Wohlmuth, Adaptive Multilevel-Finite-Elemente Methoden zur Lösung elliptischer Randwertprobleme. Ph.D. thesis, Math. Inst., TU München (1995). Zbl0849.65091
  21. [21] D. Yu, Asymptotically exact a posteriori error estimators for elements of bi-odd degree. Chinese J. Numer. Math. Appl. 13(1991) 64-78. Zbl0850.65200MR1136156
  22. [22] D. Yu, Asymptotically exact a posteriori error estimator for elements of bi-even degree. Chinese J. Numer. Math. Appl. 13 (1991) 82-90. Zbl0850.65197MR1258636

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