Quasi-interpolation and a posteriori error analysis in finite element methods
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 6, pp. 1187-1202. 
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     author = {Carstensen, Carsten},
     title = {Quasi-interpolation and a posteriori error analysis in finite element methods},
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     pages = {1187--1202},
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     volume = {33},
     number = {6},
     year = {1999},
     mrnumber = {1736895},
     zbl = {0948.65113},
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     url = {http://archive.numdam.org/item/M2AN_1999__33_6_1187_0/}
}
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Carstensen, Carsten. Quasi-interpolation and a posteriori error analysis in finite element methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 6, pp. 1187-1202. http://archive.numdam.org/item/M2AN_1999__33_6_1187_0/

[1] A. Alonso, Error estimators for a mixed method. Numer. Math. 74 (1996) 385-395. | MR | Zbl

[2] I. Babu&Amp;#0161;Ka and W.C. Rheinboldt, Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978). | MR | Zbl

[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. | MR | Zbl

[4] D. Braess, Finite Eléments. Cambridge University Press (1997). | MR | Zbl

[5] D. Braess and R. Verfürth, A posteriori error estimators for the Raviart-Thomas element. SIAM J. Numer. Anal. 33 (1996) 2431-2444. | MR | Zbl

[6] S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Texts Appl. Math. 15, Springer, New-York (1994). | MR | Zbl

[7] F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag (1991). | MR | Zbl

[8] C. Carstensen, A posteriori error estimate for themixed finite element method. Math. Comp. 66 (1997) 465-476. | MR | Zbl

[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). | Zbl

[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). | Zbl

[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). | Zbl

[12] P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. | Numdam | MR | Zbl

[13] P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1978). | MR | Zbl

[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. | Numdam | MR | Zbl

[15] K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations. Acta Numer.4 (1995) 105-158. | MR | Zbl

[16] V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer, Berlin (1986). | MR | Zbl

[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. | Numdam | MR | Zbl

[18] R. Temam, Theory and Numerical Analysis of the Navier-Stokes Equations. North-Holland (1977). | MR | Zbl

[19] R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley-Teubner (1996). | Zbl

[20] B. Wohlmuth, Adaptive Multilevel-Finite-Elemente Methoden zur Lösung elliptischer Randwertprobleme. Ph.D. thesis, Math. Inst., TU München (1995). | Zbl

[21] D. Yu, Asymptotically exact a posteriori error estimators for elements of bi-odd degree. Chinese J. Numer. Math. Appl. 13(1991) 64-78. | MR | Zbl

[22] D. Yu, Asymptotically exact a posteriori error estimator for elements of bi-even degree. Chinese J. Numer. Math. Appl. 13 (1991) 82-90. | MR | Zbl