An Introduction to Uncertainty Quantification for Kinetic Equations and Related Problems

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11 Scopus citations

Abstract

We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction details or incomplete information at the boundaries or on the initial data. These uncertainties contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge. After a brief introduction on the main numerical techniques for uncertainty quantification in partial differential equations, we focus our survey on some of the recent progress on multi-fidelity methods and stochastic Galerkin methods for kinetic equations.

Original languageEnglish
Title of host publicationSEMA SIMAI Springer Series
PublisherSpringer Science and Business Media Deutschland GmbH
Pages141-181
Number of pages41
DOIs
StatePublished - 2021
Externally publishedYes

Publication series

NameSEMA SIMAI Springer Series
Volume25
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

Keywords

  • Boltzmann equation
  • Euler equations
  • Kinetic models
  • Multi-fidelity methods
  • Stochastic Galerkin methods
  • Uncertainty quantification

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