Error estimation based on superconvergent patch recovery using statically admissible stress fields

International Journal for Numerical Methods in Engineering

Volumn 42, Issue 3, 1998, Pages 443-472

  Kvamsdal, Trond ^a,b   Okstad, Knut Morten ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b SINTEF   (Norway)

Author keywords

Error estimation; Finite element method; Stress recovery

Indexed keywords

BOUNDARY CONDITIONS; ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; STRAIN;

STRESS RECOVERY;

STRESS ANALYSIS;

EID: 0032098195     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980615)42:3<443::AID-NME366>3.0.CO;2-G     Document Type: Article

References (22)

1. I. Babuška and W. C. Rheinboldt, 'Error estimates for adaptive finite element computations', SIAM. J. Numer. Anal., 15, 736-754 (1978).
2. I. Babuška and W. C. Rheinboldt, 'A-posteriori error estimates for the finite element method', Int. J. Numer. Meth. Engng., 12, 1597-1615 (1978).
3. I. Babuška, 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. Meth. Appl. Mech, Engng., 114, 307-378 (1994).
4. I. Babuška and A. Miller, 'The post-processing approach in the finite element method - part 1: calculation of displacements, stresses and other higher derivatives of the displacements'. Int. J. Numer. Meth. Engng., 20, 1085-1109 (1984).
5. I. Babuška and A. Miller, 'The post-processing approach in the finite element method - part 2: the calculation of stress intensity factors', Int. J. Numer. Meth. Engng., 20, 1111-1129 (1984).
6. I. Babuška and A. Miller, 'The post-processing approach in the finite element method - part 3: a posteriori error estimates and adaptive mesh selection'. Int. J. Numer. Meth. Engng., 20, 2311-2324 (1984).
7. I. Babuška, T. Strouboulis, C. S. Upadhyay, S. K. Gangaraj and K. Copps, 'Validation of a posteriori error estimators by numerical approach', Int. J. Numer. Meth. Engng., 37, 1073-1123 (1994).
8. O. C. Zienkiewicz and J. Z. Zhu, 'The superconvergent patch recovery and a posteriori error estimates. Part I. the recovery technique', Int. J. Numer. Meth. Engng., 33, 1331-1364 (1992).
9. O. C. Zienkiewicz and J. Z. Zhu, 'The superconvergent patch recovery and a posteriori error estimates. Part 2: error estimates and adaptivity', Int. J. Numer. Meth. Engng., 33, 1365-1382 (1992).
10. J. Barlow, 'Optimal stress locations in finite element models', Int. J. Numer. Meth. Engng., 10, 243-251 (1976).
11. N.-E. Wiberg and F. Abdulwahab, 'Patch recovery based on superconvergent derivatives and equilibrium', Int. J. Numer. Meth. Engng., 36, 2703-2724 (1993).
12. 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).
13. T. Blacker and T. Belytschko, 'Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements', Int. J Numer. Meth. Engng., 37, 517-536 (1994).
14. M. Ainsworth and A. Craig, 'A posteriori error estimators in the finite element method', Numer. Math., 60, 429-463 (1992).
15. M. Ainsworth, J. Z. Zhu, A. W. Craig and O. C. Zienkiewicz, 'Analysis of the Zienkiewicz-Zhu a-posteriori error estimator in the finite element method', Int. J. Numer. Meth. Engng., 28, 2161-2174 (1989).
16. J. T. Oden and G. F. Carey, Finite Elements: Mathematical Aspects, vol. IV, Prentice-Hall, Englewood Cliffs, N.J., U.S.A., 1983.
17. B. Szabó and I. Babuška, Finite Element Analysis, Wiley, New York, U.S.A., 1991.
18. P. Coorevits, P. Ladeveze and J.-P. Pelle, 'An automatic procedure with a control of accuracy for finite element analysis in 2D elasticity', Comput. Meth. Appl. Mech. Engng., 121, 91-120 (1995).
19. O. C. Zienkiewicz, J. Z. Zhu and J. Wu, 'Superconvergent patch recovery Techniques - some further tests', Commun. Numer. Meth. Engng., 9, 251-258 (1993)
20. A. C. A. Ramsay and H. Sbresny, 'Evaluation of some error estimators for the four-noded Lagrangian quadrilateral', Commun. Numer. Meth. Engng., 11, 497-506 (1995).
21. M. S. Shephard and M. K. Georges, 'Automatic three-dimensional mesh generation by the finite octree technique', Int. J. Numer. Meth. Engng., 32, 709-749 (1991).
22. K. M. Okstad, 'Adaptive methods for nonlinear finite element analysis of shell structures', Dr. Ing. Dissertation, Department of Structural Engineering, The Norwegian Institute of Technology, Trondheim, Norway, 1994.