A posteriori error estimates for nonconforming finite element methods

Numerische Mathematik

Volumn 92, Issue 2, 2002, Pages 233-256

  Carstensen, Carsten ^a   Bartels, Sören ^b   Jansche, Stefan ^b  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF KIEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035982256     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100378     Document Type: Article

References (22)

1. [A] A. Alonso: Error estimators for a mixed method. Numer. Math. 74 (1996) 385-395
2. [BC] S. Bartels, C. Carstensen: Each Averaging Technique Yields Reliable A Posteriori Error Control in FEM on Unstructured Grids. Part IT: Higher Order FEM. Math. Comp. (2002) Accepted for publication (http://www.numerik.unikiel.de/reports/2000/00-5.html)
3. [BS] S.C. Brenner, L.R. Scott: The Mathematical Theory of Finite Element Methods. Texts Appl. Math. 15, Springer, New-York, 1994
4. C. Carstensen: A posteriori error estimate for the mixed finite element method, Math. Comp. 66 (1997) 465-476
5. [C2] C. Carstensen: Quasi interpolation and a posteriori error analysis in finite element method. Math. Modelling Numer. Anal. 33 (1999) 1187-1202
6. [CB] C. Carstensen, 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. (2002). In press (http://www.numerik.uni-kiel.de/reports/1999/99-11.html)
7. [CF] C. Carstensen, S.A. Funken: Constants in Clément-interpolation error and residual based a posteriori error estimates in Finite Element Methods. East-West Journal of Numerical Analysis 8 (3) (2000) 153-175
8. [Ci] P.O. Ciarlet: The finite element method for elliptic problems. North-Holland, Amsterdam, 1978
9. [Cl] P. Clément: Approximation by finite element functions using local regularization. RAIRO Sén Rouge Anal. Numér. R-2 (1975) 77-84
10. [DDPV] 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
11. [EEHJ] K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Introduction to adaptive methods for differential equations. Acta Numerica (1995) 105-158
12. [GR] V. Girault, P.A. Raviart: Finite Element Methods for Navier-Stokes Equations. Springer, Berlin, 1986
13. [G] P. Grisvard: Elliptic Problems in Nonsmooth Domains. Pitman, Boston, 1985
14. [H] L. Hörmander: Linear partial differential operators. Springer, Berlin, 1963
15. [HW] R.H.W. Hoppe, B. Wohlmuth: Element-orientated and edge-orientated local error estimates for noncoforming finite element methods. Math. Modelling Numer. Anal. 30 (1996) 237-263
16. [KS] G. Kanschat, F.-T. Suttmeier: A posteriori error estimates for nonconforming finite element schemes. Calcolo 36, No.3, 129-141 (1999)
17. [LM] J.L Lions, E. Magenes: Non-homogeneous boundary value problems and applications, Vol. I. Springer, Berlin, 1972
18. [RT] R. Rannacher, S. Turek: Simple nonconforming quadrilateral stokes element. Num. Meth. PDE, 8(2) (1992) 97-111
19. [SF] G. Strang, G.J. Fix: An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, 1973
20. [V1] R. Verfürth: A posteriori error estimates and adaptive mesh-refinement techniques. J. Comput. Appl. Math. 50 (1994) 67-83
21. [V2] R. Verfürth: A review of a posteriori error estimation and adaptive mesh-refinement techniques. Teubner Skripten zur Numerik, Teubner, Stuttgart 1996
22. [W] B. Wohlmuth: Adaptive Multilevel-Finite-Elemente Methoden zur Lösung elliptischer Randwertprobleme. PhD Thesis, Math. Inst., TU München, München, 1995