Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A modified Zienkiewicz-Zhu error estimator

  • Stephen, D.B. (Department of Aeronautical Engineering, University of Sydney) ;
  • Steven, G.P. (Department of Aeronautical Engineering, University of Sydney)
  • Published : 1996.01.25
⟨ Previous Next ⟩

Abstract

A new error measure for a static finite element analysis is proposed. This error measure is a modification to the Zienkiewicz and Zhu energy norm. The new error estimator is a global error measure for the analysis and is independent of finite element model size and internal stresses, hence it is readily transportable to other error calculations. It is shown in this paper the the new error estimator also produces conservative error measurements, making it a suitable procedure to adopt in commerical packages.

Keywords

References

  1. Ainsworth, M., Zhu, J. Z., Craig, A.W. and Zienkiewicz, O.C. (1989), "Analysis of the Zienkiewicz-Zhua-posteriori error estimator in the finite element method", International Journal of Numerical Methods in Engineering, 28, 2161-2174. https://doi.org/10.1002/nme.1620280912
  2. Barlow, J. (1976), "Optimal stress location in finite element method," International Journal of Numerical Methods in Engineering, 10, 243-251. https://doi.org/10.1002/nme.1620100202
  3. Hinton, E. and Campbell, J.S. (1974), "Local global smoothing of discontinuous finite element functions using a least square method", International Journal of Numerical Methods in Engineering, 8, 461-480. https://doi.org/10.1002/nme.1620080303
  4. Rank, E. and Zienkiewicz, O.C. (1987), "A simple error estimator in the finite element method", Communications in Applied Numerical Methods, 3, 243-247.
  5. Sokolnikoff, I.S. (1957), "Mathematical theory elasticity", McGraw-Hill Book Company, Inc. New York.
  6. Wieberg, N-E. and Li, X.D. (1994), "Superconvergent patch recovery of finite element solution and a posteriori $L_2$ norm error estimate", Communications in Numerical Methods in Engineering, 10, 313-320. https://doi.org/10.1002/cnm.1640100406
  7. Zienkiewicz, O.C. and Zhu, J.Z. (1987), "A simple error estimator and adaptive procedure for practical engineering analysis", International Journal of Numerical Methods in Engineering, 24, 337-357. https://doi.org/10.1002/nme.1620240206
  8. Zienkiewicz, O.C. and Zhu, J.Z. (1992), "Superconvergent patch recovery and a posteriori error estimates. Part 1: The rescovery technique", International Journal of Numerical Methods in Engineering, 33, 1331-1364. https://doi.org/10.1002/nme.1620330702
  9. Zienkiewicz, O.C. and Zhu, J.Z. (1992), "The superconvergent patch recovery and posteriori error estimates. part 2: Error estimates an adaptivity", International Journal of Numerical Methods in Engineering, 33, 1331-1364. https://doi.org/10.1002/nme.1620330702

Cited by

  1. Improved stress recovery for elements at boundaries vol.5, pp.2, 1997, https://doi.org/10.12989/sem.1997.5.2.127
  2. Error estimates and adaptive finite element methods vol.18, pp.5/6, 2001, https://doi.org/10.1108/EUM0000000005788