Method for treating discretization error in nondeterministic analysis

AIAA journal

Volumn 38, Issue 5, 2000, Pages 910-916

  Alvin, Kenneth F ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; FAILURE ANALYSIS; INTERPOLATION; MONTE CARLO METHODS; RELIABILITY;

DISCRETIZATION ERROR; NONDETERMINISTIC ANALYSIS; RESPONSE SURFACE METHOD;

ERROR ANALYSIS;

EID: 0034188390     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.1047     Document Type: Article

References (18)

1. Zienkiewicz, O. C., and Zhu, J. Z., "A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis," International Journal for Numerical Methods in Engineering, Vol. 27, No. 2, 1987, pp. 337-357.
2. Babuska, I., Strouboulis, T., Upadhyay, C. S., Gangaraj, S. K., and Copps, K., "Validation of A Posteriori Error Estimators by Numerical Approach," International Journal for Numerical Methods in Engineering, Vol. 37, No. 7, 1994, pp. 1073-1123.
3. Richardson, L. F., "The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations with an Application to the Stresses in a Masonry Dam," Transactions of the Royal Society of London, Series A, Vol. 210, 1910, pp. 307-357.
4. Richards, S. A., "Completed Richardson Extrapolation in Space and Time," Communications in Numerical Methods in Engineering, Vol. 13, No. 7, 1997, pp. 573-582.
5. Roache, P. J., Verification and Validation in Computational Science and Engineering, Hermosa, Albuquerque, NM, 1998, pp. 108-136.
6. Issacson, E., and Keller, H. B., Analysis of Numerical Methods, Wiley, New York, 1966, pp. 364-383.
7. Iserles, A., Numerical Analysis of Differential Equations, Cambridge Univ. Press, Cambridge, England, U.K., 1996, pp. 7, 8.
8. Hughes, T. J. R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987, pp. 188-190.
9. Strang, G., and Fix, G. J., An Analysis of the Finite Element Method, Wellesley-Cambridge, Wellesley, MA, 1988, pp. 165-171.
10. Cook, R. D., Malkus, D. S., and Plesha, M. E., Concepts and Applications of Finite Element Analysis, 3rd ed., Wiley, New York, 1989, pp. 553-563.
11. Montgomery, D. C., Design and Analysis of Experiments, 3rd ed., Wiley, New York, 1991.
12. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P., "Design and Analysis of Computer Experiments," Statistical Science, Vol. 4, No. 4, 1989, pp. 409-435.
13. Romero, V. J., and Bankston, S. D., "Finite-Element/Progressive-Lattice-Sampling Response Surface Methodology and Application to Benchmark Probability Quantification Problems," Sandia National Labs., Rcpt. SAND98-0567, Albuquerque, NM, March 1998.
14. Fox, E. P., "Issues in Utilizing Response Surface Methodologies for Accurate Probabilistic Design," Proceedings of the AIAA 37th Structures, Structural Dynamics, and Materials Conference, AIAA, Reston, VA, 1996, pp. 1615-1622.
15. Kammer, D. C., "Sensor Placement for On-Orbit Modal Identification and Correlation of Large Space Structures," Journal of Guidance, Control, and Dynamics, Vol. 14, No. 2, 1991, pp. 251-259.
16. Red-Horse, J. R., "Modal Experiment Design Using Subset Selection," Proceedings of the 14th International Modal Analysis Conference, Society for Experimental Mechanics, Bethel, CT, 1996.
17. Oberkampf, W. L., and Blottner, F. G., "Issues in Computational Fluid Dynamics Code Verification and Validation," AIAA Journal, Vol. 36, No. 5, 1998, pp. 687-695.
18. Weaver, W., Timoshenko, S. P., and Young, D. H., Vibration Problems in Engineering, 5th ed., Wiley, New York, 1990, pp. 369-370.