Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty

J. Tinsley Oden; Ivo Babuška; Fabio Nobile; Yusheng Feng; Raul Tempone

doi:10.1016/j.cma.2003.06.003

Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty

J. Tinsley Oden^*, Ivo Babuška, Fabio Nobile, Yusheng Feng, Raul Tempone

^*Corresponding author for this work

Computer, Electrical and Mathematical Science and Engineering

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented.

Original language	English (US)
Pages (from-to)	195-204
Number of pages	10
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	194
Issue number	2-5 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.cma.2003.06.003
State	Published - Feb 4 2005

Keywords

Adaptive modeling
Modeling error estimation
Stochastic partial differential equations

ASJC Scopus subject areas

Computer Science Applications
Computational Mechanics

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10.1016/j.cma.2003.06.003

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abstract = "The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented.",

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AU - Babuška, Ivo

AU - Nobile, Fabio

AU - Feng, Yusheng

AU - Tempone, Raul

PY - 2005/2/4

Y1 - 2005/2/4

N2 - The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented.

AB - The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented.

KW - Adaptive modeling

KW - Modeling error estimation

KW - Stochastic partial differential equations

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IS - 2-5 SPEC. ISS.

ER -

Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty

Abstract

Keywords

ASJC Scopus subject areas

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