The reliability of computer predictions: Can they be trusted?

International Journal of Numerical Analysis and Modeling

Volumn 3, Issue 3, 2006, Pages 255-272

  Babuška, Ivo ^a   Oden, J Tinsley ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Computer simulations; Validation; Verification

Indexed keywords

EID: 77949535330     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (44)

1. Ainsworth, M. and Oden, J.T. A Posteriori Error Estimation in Finite Element Analysis, John Wiley and Sons, New York, 2000.
2. Aluminum Association, Aluminum Standards and Data, pp. 108-109, 1984.
3. American Society for Metals, Metals Handbook, Properties and Selection, Nonferrous Alloys and Pure Metals, Vol. 2, pp. 109-110, 1979.
4. Ayyub, B.M. Elicitation of Expert Opinions for Uncertainty and Risk, CRC Press, 2001.
5. Babuška, I. On Randomized Laplace’s Equation, Casopis Pest. Mat, Vol. 86, pp. 269-276, 1961.
6. Babuška, I. and Chatzipantelidis, P. On Solving Elliptic Stochastic Differential Equations, Computer Methods in Applied Mechanics and Engineering, Vol. 191, pp. 4093-4122, 2002.
7. Babuška, I. and Chleboun, J. Effects of the Uncertainties in the Domain on the Solution Neumann Boundary Value Problems in Two Spacial Dimensions, Math. Comp., 71(240), pp. 1339-1370, 2002.
8. Babuška, I., Jerina, K., Li, Y., and Smith, P. Quantitative Assessment of the Accuracy of Constitutive Laws for Plasticity with Emphasis on Cyclic Deformation, Material Parameter Estimation for Modern Constitutive Equations, Bertram, L.A., Brown, S.B., and Freed, A.D. (Eds.), American Society of Mechanical Engineers, pp. 113-171, 1993.
9. Babuška, I., Liu, K.M., and Tempone, R. Solving Stochastic Partial Differential Equations Based on Experimental Data, Math. Models Methods in Appl. Sci., Vol. 13, pp. 415-444, 2003.
10. Babuška, I., Nobile, F., and Tempone, R. Worst Case Scenario Analysis for Elliptic Problems with Uncertainty, The University of Texas, ICES Report, Accepted Numer. Math, pp. 4-36, 2004.
11. Babuška, I. and Oden, J.T. Verification and Validation in Computational Engineering and Science, Part 1, Basic Concepts”, Computer Methods in Applied Mechanics and Engineering, 193, pp. 4047-4066, 2004.
12. Babuška, I. and Rheinboldt, W.C. A Posteriori Error Estimated for the Finite Element Method, J. Numer. Math. Engrg., 12, pp. 1597-1615, 1978.
13. Babuška, I. and Strouboulis, T. The Finite Element Method and its Reliability, Oxford University Press, Oxford, 2001.
14. Babuška, I., Tempone, R., and Zouraris, G.E. Galerkin Finite Element Approximations of Stochastic Elliptic Differential Equations, SIAM J. Numer. Anal., Vol. 42, pp. 800-825, 2004.
15. Babuška, I, Tempone, R., and Zouraris, G.E. Solving Elliptic Boundary Value Problems with Uncertain Coefficients by the Finite Element Method: The Stochastic Formulation, Computer Methods in Applied Mechanics and Engineering, Vol. 194, pp. 1251-1294, 2004.
16. Ben-Haiman, Y. and Hermez, F.M. Robustness, Fidelity and Prediction-Looseness of Models, ESDA 2004-58008, Proceedings of ESDA 04, 7th Biennial Conference on Engineering System Design and Analysis, Manchester, UK, 2004.
17. Bertram, L.A., Brown, S.B., and Freed, A.D., (Eds.) Material Parameter Estimation for Modern Constitutive Equations, American Society of Mechanical Engineers, 1993.
18. Chaboche, J.L. The Independent Constitutive Theories for Cyclic Plasticity, International Journal of Plasticity 2, pp. 149-189, 1986.
19. Cullen, A.C. and Frey, H.C. Probabilistic Techniques Expose Assesment, Plenum Press, 1999.
20. Elishakoff, I. Whys and Hows in Uncertainty, Modeling, Probability, Fuzziness and Anti-Optimization, CISM Courses and Lectures, N 388, Springer, 1999.
21. Frank, M.D. The Physical Limits of Computing, Computing in Science and Engineering, Vol. 4, pp. 16-26, 2002.
22. Frauenfelder, P. Schwab, C., and Todor, R.A. Finite Elements for Elliptic Problems with Stochastic Coefficients, to appear in Computer Methods in Applied Mechanics and Engineering, 2005.
23. Guide for Verification and Validation of Computational Fluid Dynamics Simulation, TECH REP, AIAA G-077-1998, American Institute of Aeronautics and Astronautics, 1998.
24. Hadipriono, F.C. Fuzzy Set in Probabilistic Structural Mechanics, Probabilistic Engineering Handbook, Theory and Industrial Applications, Sundararayan, C. (Ed.), Chapman and Hall, New York, pp. 280-316, 1995.
25. Han, W. and Reddy, B.D. Plasticity, Mathematical Theory and Numerical Analysis, Springer Verlag, Berlin, 1999.
26. Helton, J.C., Johnson, J.D., and Oberkampf, W.L. An Exploration of Alternative Approaches to the Representation, of Uncertainty in Model Prediction, Reliability Engineering and System Safety, Vol. 85, pp. 39-71, 2004.
27. Hlavacek, I., Chleboun, J., and Babuška, I. Uncertain Input Data Problems and the Worst Scenario Method, Elsevier, 2005.
28. Johnson, C. On Plasticity with Hardening, Journal of Math, Analysis and Applications, Vol. 62, pp. 326-336, 1978.
29. Klir, G.J., St. Clair, U.H., and Yuan, B. Fuzzy Set Theory: Foundations and Applications, Foundations and Applications, Prentice Hall, 1997.
30. Li, Y. and Babuška, I. A Convergence Analysis of H-Version Finite-Element Method with High Order Elements for Two-Dimensional Elasto-Plasticity Problems, SIAM J. Numer. Anal., Vol. 34, pp. 998-1036, 1997.
31. Material and Elements for Aerospace Vehicle Structures, Mil-HDBK-58, January 2003.
32. Miyoshi, T. Foundations of the Numerical Analysis of Plasticity, Lecture Notes in Numerical and Applied Analysis 7, North Holland, Amsterdam, 1985.
33. Oberkampf, W.L. and Trucano, T.G. Verification and Validation in Computational Fluid Dynamics, Progress in Aerospace Sciences, Vol.38, pp. 209-272, 2002.
34. Oden, J.T. The Promise of Computational Engineering and Science: Will it be kept?, Expressions, No. 12, pp. 12-15, 2002.
35. Oden, J.T. and Prudhomme, S. Estimation of Modeling Error in Computational Mechanics, J. of Comp. Phy., Vol. 182, pp. 496-515, 2002.
36. Oden, J.T. and Vemaganti, K.S. Estimation of Local Modeling Error and Goal-Oriented Adaptive Modeling of Heterogeneous Materials. Part 1: Error Estimates and Adaptive Algorithms, J. of Comp. Phy., Vol. 164, pp. 22-47, 2000.
37. Popper, K. The Logic of Scientific Discovery, Rutlege Classics, Taylor and Frances Group, 2003.
38. Post, D.E. The Coming Crisis in Computational Science, Los Alamos National Laboratory, Rep LA-UR-0388, 2004.
39. Roache, P.J. Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, New Mexico, 1998.
40. Schwab, C. and Todor, R.A. Sparse Finite Elements for Elliptic Problems-Higher Order Moments, ETH Zurich, Report 2003-2004, Seminar Angewandte Mathematics, 2003.
41. Schwab, C. and Todor, R.A. Sparse Finite Elements for Elliptic Problems with Stochastic Loading, Numer. Math., Vol. 95, pp. 707-734, 2003.
42. Szabo, B.A. and Muntges, D. Procedures for the Verification and Validation of Working Models for Structural Shells, Proceedings of IMECE 2004, Numer. Math., 93, pp. 583-610, 2003.
43. Wong, W.A., Bucci, R.J., Stenz, R.H., and Conway, J.B. Controlled Fatigue Data for Certain Aluminum Alloys for Applications in the Transportation Industry, SAE Technical Paper Series, No. 870094, International Congress and Exposition, 1987.
44. Zuckowski, M. Combined Loading in the Theory of Plasticity, PWN-Polish Scientific Publishers, Warszawa, 1998.