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On the role of hierarchic spaces and models in verification and validation. (English) Zbl 1157.65495

Summary: An overview of the general considerations underlying the selection of mathematical models and the methods used for estimation and control of the associated errors and the requisite technical capabilities are presented. An example that illustrates the main points of the paper is presented.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
93C40 Adaptive control/observation systems
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[1] Guide for Verification and Validation in Computational Solid Mechanics, The American Society of Mechanical Engineers, New York, V&V 10-2006, ISBN No: 079183042X, 2006.; Guide for Verification and Validation in Computational Solid Mechanics, The American Society of Mechanical Engineers, New York, V&V 10-2006, ISBN No: 079183042X, 2006.
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[3] Szabó, B.; Muntges, D., Procedures for the verification and validation of working models for structural shells, J. Appl. Mech., 72, 907-915 (2005) · Zbl 1111.74656
[4] Szabó, B.; Düster, A.; Rank, E., The \(p\)-version of the finite element method, (Stein, E.; de Borst, R.; Hughes, T. J.R., Encyclopedia of Computational Mechanics, vol. 1 (2004), John Wiley & Sons: John Wiley & Sons Chichester), (Chapter 5) · Zbl 1114.74486
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[7] B.A. Szabó, R.L. Actis, S.M. Holzer, Solution of elastic-plastic stress analysis problems by the \(p\); B.A. Szabó, R.L. Actis, S.M. Holzer, Solution of elastic-plastic stress analysis problems by the \(p\)
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