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Polynomial Chaos Methods for Hyperbolic Partial Differential EquationsIntroduction

Polynomial Chaos Methods for Hyperbolic Partial Differential Equations: Introduction [In many physical problems, knowledge is limited in quality and quantity by variability, bias in the measurements and limitations in the measurements: these are all sources of uncertaintiesuncertainties. When we attempt to solve the problem numerically, we must account for those limitations, and in addition, we must identify possible shortcomings in the numerical techniques employed. Incomplete understanding of the physical processes involved will add to the sources of possible uncertainty in the models employed. In a general sense, we distinguish between errors and uncertainty simply by saying that errors are recognizable deficiencies not due to lack of knowledge, whereas uncertainties are potential and directly related to lack of knowledge [1]. This definition clearly identifies errors as deterministic quantities and uncertainties as stochastic in nature; uncertainty estimation and quantification are, therefore, typically treated within a probabilistic framework.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Polynomial Chaos Methods for Hyperbolic Partial Differential EquationsIntroduction

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2015
ISBN
978-3-319-10713-4
Pages
3 –9
DOI
10.1007/978-3-319-10714-1_1
Publisher site
See Chapter on Publisher Site

Abstract

[In many physical problems, knowledge is limited in quality and quantity by variability, bias in the measurements and limitations in the measurements: these are all sources of uncertaintiesuncertainties. When we attempt to solve the problem numerically, we must account for those limitations, and in addition, we must identify possible shortcomings in the numerical techniques employed. Incomplete understanding of the physical processes involved will add to the sources of possible uncertainty in the models employed. In a general sense, we distinguish between errors and uncertainty simply by saying that errors are recognizable deficiencies not due to lack of knowledge, whereas uncertainties are potential and directly related to lack of knowledge [1]. This definition clearly identifies errors as deterministic quantities and uncertainties as stochastic in nature; uncertainty estimation and quantification are, therefore, typically treated within a probabilistic framework.]

Published: Sep 17, 2014

Keywords: Polynomial Chaos; Polynomial Chaos Expansion; Input Uncertainty; Stochastic Input; Characteristic Boundary Condition

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