The relationship of some a posteriori estimators

Computer Methods in Applied Mechanics and Engineering

Volumn 176, Issue 1-4, 1999, Pages 463-475

  Zhu, J Z ^a   Zhang, Zhimin ^b  

^a UES Software Inc   (United States)

^b TEXAS TECH UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; ESTIMATION; PROBLEM SOLVING;

RECOVERY ERROR ESTIMATORS; RESIDUAL ERROR ESTIMATORS;

ERROR ANALYSIS;

EID: 0032687062     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00349-1     Document Type: Article

References (29)

1. [1] I. Babuska and W.C. Rheinboldt, A posteriori error estimates for the finite element method, Int. J. Numer. Methods Engrg. 12 (1978) 1597-1615.
2. [2] I. Babuska and W.C. Rheinboldt, Reliable error estimation and mesh adaptation for the finite element method, in: J.T. Oden, ed., Computational Method in Nonlinear Mechanics (North Holland, Amsterdam, 1980) 67-108.
3. [3] I. Babuska and W. C. Rheinboldt, A posteriori error analysis of finite element solutions for one-dimensional problems, SIAM J. Numer. Anal. 18 (1981) 565-589.
4. [4] O.C. Zienkiewicz, J.P. Gago and D.W. Kelly, The hierarchical concept in the finite element method, Comput. Struct. 16 (1983) 53-65.
5. [5] D.W. Kelly, J.R. Gago, O.C. Zienkiewicz and I. Babuska, A posteriori error analysis and adaptive processes in the finite element method. Part I: error analysis, Int. J. Numer Methods Engrg. 19 (1983) 1593-1619.
6. [6] P. Ladeveze and D. Leguillon, Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal. 20 (1983) 485-509.
7. [7] D.W. Kelly, The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method, Int. J. Numer. Methods Engrg., 20 (1984) 1491-1506.
8. [8] R.E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comput. 44 (1985) 283-301.
9. [9] I. Babuska and A. Miller, A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator, Comput. Methods Appl. Mech. Engrg. 61 (1987) 1-40.
10. [10] J.T. Oden, L. Demkowicz, W. Rachowicz and T.A. Westermann, Toward a universal h-p adaptive finite element strategy. Part 2: a posteriori error estimation, Comput. Methods Appl. Mech. Engrg. 77 (1989) 113-180.
11. [11] R. Verfurth, A posteriori error estimators for the Stokes equations, Numer. Math. 55 (1989) 309-325.
12. [12] C. Johnson and P. Hansbo, Adaptive finite element methods in computational mechanics, Comput. Methods Appl. Mech. Engrg. 101 (1982) 143-181.
13. [13] M. Ainsworth and J.T. Oden, A unified approach to a posteriori estimation using element residual methods, Numer. Math. 65, (1993) 23-50.
14. [14] O.C. Zienkiewicz and J.Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Methods Engrg. 24 (1987) 337-357.
15. [15] J.Z. Zhu and O.C. Zienkiewicz, Superconvergent recovery technique and a posteriori error estimators, Int. J. Numer. Methods Engrg. 30 (1990) 1321-1340.
16. [16] O.C. Zienkiewicz and J.Z. Zhu, Superconvergent patch recovery and a posteriori error estimates. Part I: The recovery technique, Int. J. Numer. Methods Engrg. 33 (1992) 1331-1364.
17. [17] O.C. Zienkiewicz and J.Z. Zhu, Superconvergent patch recovery and a posteriori error estimates. Part II: Error estimates and adaptivity, Int. J. Numer. Methods Engrg. 33 (1992) 1365-1382.
18. [18] O.C. Zienkiewicz and J.Z. Zhu, Superconvergent patch recovery (SPR) and adaptive finite element refinement, Comput. Methods Appl. Mech. Engrg. 101 (1992) 207-224.
19. [19] N.E. Wiberg and F. Abdulwahab, Patch recovery based on superconvergent derivatives and equilibrium, Int. J. Numer. Methods Engrg. 36 (1993) 2703-2724.
20. [20] T. Blacker and T. Belychko, Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements, Int. J. Numer. Methods Engrg. 37 (1994) 517-536.
21. [21] E. Rank and O.C. Zienkiewicz, A simple error estimator in the finite element method, Comm. Appl. Numer. Methods, 3 (1987) 243-249.
22. [22] R. Rodriguez, Some remarks on Zienkiewicz-Zhu estimator, Int. J. Numer. Methods PDE 10 (1994) 625-635.
23. [23] J.Z. Zhu, A posteriori error estimation - the relationship between different procedures, Comput. Methods Appl. Mech. Engrg. 150 (1997) 411-422.
24. [24] O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, 4th edition, Vol. 1: Basic Formulation and Linear Problems (McGraw-Hill, London, 1989).
25. [25] Z. Zhang, Ultraconvergence of the patch recovery technique, Math. Comput. 65 (1996) 1431-1437.
26. [26] L.B. Wahlbin, Local behavior in finite element methods, in: P.G. Ciarlete and J.L. Lions, eds., Handbook of Numerical Analysis, Vol. II (North-Holland, Amsterdam, 1991) 357-522.
27. [27] I. Babuska, 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.
28. [28] I. Babuska, T. Strouboulis, C.S. Upadhyay, S. K. Gangaraj and K. Copps, Validation of a posteriori error estimators by numerical approach, Int. J. Numer. Methods Engrg. 37 (1994) 1073-1123.
29. [29] I. Babuska, T. Strouboulis and C.S. Upadhyay, A model study of a posteriori error estimators for linear elliptic problems. Part II: Error estimation at the boundary of patchwise uniform grids of triangles, to be published.