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Introduction

  • Mass Per Pettersson
  • Gianluca Iaccarino
  • Jan Nordström
Chapter
Part of the Mathematical Engineering book series (MATHENGIN)

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.

Keywords

Polynomial Chaos Polynomial Chaos Expansion Input Uncertainty Stochastic Input Characteristic Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mass Per Pettersson
    • 1
  • Gianluca Iaccarino
    • 2
  • Jan Nordström
    • 3
  1. 1.Uni ResearchBergenNorway
  2. 2.Department of Mechanical Engineering and Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  3. 3.Department of Mathematics Computational MathematicsLinköping UniversityLinköpingSweden

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