Error estimation with postprocessed finite element solutions

Computers and Structures

Volumn 64, Issue 1-4, 1997, Pages 113-137

  Wiberg, N E ^a   Abdulwahab, F ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS;

ERROR ESTIMATION; SUPERCONVERGENT PATCH RECOVERY;

FINITE ELEMENT METHOD;

EID: 0031193026     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(96)00124-1     Document Type: Article

References (25)

1. I. Babuska and W. C. Rheinboldt, A posteriori error estimates of the finite element method. Int. J. numer. Meth. Engng 12, 1597-1615 (1978).
2. O. C. Zienkiewicz and J. Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. numer. Meth. Engng 24, 333-357 (1987).
3. J. T. Oden and J. N. Reddy, Note on an approximate method for computing consistent conjugate stresses in elastic finite elements. Int. J. numer. Meth. Engng 6, 55-61 (1973).
4. E. Stein and R. Ahmad, An equilibrium method for stress calculation using finite element displacement models. Comput. Meth. appl. Mech. Engng 10, 175-198 (1977).
5. E. Hinton and J. S. Campbell, Local and global smoothing of discontinuous finite element functions using least squares method. Int. J. numer. Meth. Engng 8, 461-480 (1974).
6. O. C. Zienkiewicz and J. Z. Zhu, The superconvergent patch recovery and a posteriori error estimate. Part 1. The recovery technique. Int. J. numer. Meth. Engng 33, 1331-1364 (1992).
7. O. C. Zienkiewicz and J. Z. Zhu, The superconvergent patch recovery and a posteriori error estimators. Part 2. Error estimates and adaptivity. Int. J. numer. Meth. Engng 33, 1365-1382 (1992).
8. N.-E. Wiberg and F. Abdulwahab, Patch recovery based on superconvergent derivatives and equilibrium. Int. J. numer. Meth. Engng 36, 2703-2724 (1993).
9. N.-E. Wiberg and F. Abdulwahab, An efficient postprocessing technique for stress problems based on superconvergent derivatives and equilibrium. In: Numerical Methods in Engineering (Edited by C. H. Hirsch, J. Pesiant and W. Kordulla), pp. 25-32. Elsevier, Amsterdam (1992).
10. N.-E. Wiberg, F. Abdulwahab and S. Ziukas, Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. Int. J. numer. Meth. Engng 37, 3417-3440 (1994).
11. 2 norm error estimate. Commun. appl. numer. Meth. 10, 313-320 (1994).
12. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Technical Report, Institut für Angewandte Mathematic der Universität Zürich (1993).
13. C. Johnson and P. Hansbo, Adaptive finite element methods in computational mechanics. Comput. Meth. appl. Mech. Engng 101, 143-181 (1992).
14. J. Barlow, Optimal stress location in finite element method. Int. J. numer. Meth. Engng 10, 243-251 (1976).
15. C. M. Chen, The finite element method and the analysis of improving the accuracy (in Chinese). Human Science Press, Hunan (1982).
16. C. W. Clenshaw and J. G. Hayes, Curve and surface fitting. J. Inst. Math. Applic. 1, 164-183 (1965).
17. O. C. Zienkiewicz and J. Z. Zhu, Superconvergent patch recovery techniques - some further tests. Commun. appl. numer. Meth. 9, 251-258 (1993).
18. O. C. Zienkiewicz and J. Z. Zhu, The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput. Meth. appl. Mech. Engng 101, 207-224 (1992).
19. S. Ziukas and N.-E. Wiberg, Improved postprocessed stresses and energy norm errors for patch recovery procedures. In: Sixth Nordic Seminar on Computational Mechanics (Edited by G. Nilsson) (1993).
20. T. Blacker and T. Belytschko, Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int. J. numer. Meth. Engng 37, 517-536 (1994).
21. N.-E. Wiberg, F. Abdulwahab and S. Ziukas, Improved element stresses for node and element patches using superconvergent patch recovery. Commun. appl. numer. Meth. 11, 619-627 (1994).
22. N.-E. Wiberg and P. Möller, Formulation and solution of hierarchical finite element equations. Int. J. numer. Meth. Engng 26, 1213-1233 (1988).
23. A. Samuelsson, N.-E. Wiberg and L. F. Zeng, The effectivity of the Zienkiewicz-Zhu error estimate and two two-dimensional adaptive mesh generators. Commun. appl. numer. Meth. 9, 687-699 (1993).
24. 2 norms. Comput. Struct. 53(4), 907-919 (1994).
25. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1969).