Erratum: A posteriori error estimates on irregular grids based on gradient recovery (Advances in Computational Mathematics 15:1 (363-374) DOI:10.1023/A:1014221409940);A posteriori error estimates on irregular grids based on gradient recovery

Advances in Computational Mathematics

Volumn 15, Issue 1-4, 2001, Pages 363-374

  Zhang, Zhimin ^a  

^a WAYNE STATE UNIVERSITY   (United States)

Author keywords

A posteriori error estimate; Finite element method; Gradient recovery; ZZ patch recovery

Indexed keywords

EID: 0035563323     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-008-9090-7     Document Type: Erratum

References (20)

1. M. Ainsworth and J.T. Oden, A Posteriori Error Estimation in Finite Element Analysis (Wiley Interscience, New York, 2000).
2. I. Babuška and W.C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15(4) (1978) 736-754.
3. I. Babuška and T. Strouboulis, The Finite Element Method and its Reliability (Oxford Univ. Press, Oxford, 2001).
4. I. Babuška, T. Strouboulis and C.S. Upadhyay, A model study of the quality of a posteriori error estimators for finite element solutions of linear elliptic problems, with particular reference to the behavior near the boundary, Internat. J. Numer. Methods Engrg. 40(14) (1997) 2521-2577.
5. R. Bank, Hierarchical bases and the finite element method, Acta Numerica (1996) 1-43.
6. T. Blacker and T. Belytschko, Superconvergent patch recovery with equilibrium and cojoint interpolant enhancements, Internat. J. Numer. Methods Engrg. 37 (1994) 517-536.
7. C. Carstensen and S.A. Funken, Averaging technique for FE - a posteriori error control in elasticity. I. Conforming FEM, Comput. Methods Appl. Mech. Engrg. 190(18/19) (2001) 2483-2498.
8. C. Chen and Y. Huang, High Accuracy Theory of Finite Element Methods (Hunan Science Press, P.R. China, 1995) (in Chinese).
9. W. Dörfler and R.H. Nochetto, Small data oscillation implies the saturation assumption, preprint.
10. W. Hoffmann, A.H. Schatz, L.B. Wahlbin and G. Wittum, Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part 1: A smooth problem and globally quasi-uniform meshes, Math. Comp. 70 (2001) 897-909.
11. M. Křížek, P Neittaanmäki and R. Stenberg, eds., Finite Element Methods: Superconvergence, Post-processing, and A Posteriori Estimates, Lecture Notes in Pure and Applied Mathematics Series, Vol. 196 (Marcel Dekker, New York, 1997).
12. Q. Lin and N. Yan, Construction and Analysis of High Efficient Finite Elements (Hebei Univ. Press, P.R. China, 1996) (in Chinese).
13. R. Rodriguez, Some remarks on Zienkiewicz-Zhu estimator, Internat. J. Numer. Methods PDE 10 (1994) 625-635.
14. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, (Wiley/Teubner, Stuttgart, 1996).
15. L.B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics, Vol. 1605 (Springer, Berlin, 1995).
16. N.B. Wiberg and F. Abdulwahab, Patch recovery based on superconvergent derivatives and equilibrium, Internat. J. Numer. Mech. Engrg. 36 (1993) 2703-2724.
17. N. Yan and A. Zhou, Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes, Comput. Methods Appl. Mech. Engrg. 190 (2001) 4289-4299.
18. J.Z. Zhu and Z. Zhang, The relationship of some a posteriori error estimators, Comput. Methods Appl. Mech. Engrg. 176 (1999) 463-475.
19. O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates, Part 1: The recovery technique, Internat. J. Numer. Methods Engrg. 33 (1992) 1331-1364.
20. O.C. Zienkiewicz and J.Z. Zhu, The superconvergent patch recovery and a posteriori error estimates, Part 2: Error estimates and adaptivity, Internat. J. Numer. Methods Engrg. 33 (1992) 1365-1382.