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 uncertainties. 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.
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Pettersson, M.P., Iaccarino, G., Nordström, J. (2015). Introduction. In: Polynomial Chaos Methods for Hyperbolic Partial Differential Equations. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-10714-1_1
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