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International Journal for Uncertainty Quantification

年間 6 号発行

ISSN 印刷: 2152-5080

ISSN オンライン: 2152-5099

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ERROR ESTIMATE OF A BIFIDELITY METHOD FOR KINETIC EQUATIONS WITH RANDOM PARAMETERS AND MULTIPLE SCALES

巻 11, 発行 5, 2021, pp. 57-75
DOI: 10.1615/Int.J.UncertaintyQuantification.2021032770
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要約

In this paper, we conduct uniform error estimates of the bifidelity method for multiscale kinetic equations. We take the Boltzmann and the linear transport equations as important examples, and discuss various choices of low-fidelity models for more general kinetic equations. The main analytic tool is the hypocoercivity analysis for kinetic equations, considering solutions in a perturbative setting close to the global equilibrium. This allows us to obtain the error estimates in both kinetic and hydrodynamic regimes.

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によって引用された
  1. Liu Liu, Pareschi Lorenzo, Zhu Xueyu, A bi-fidelity stochastic collocation method for transport equations with diffusive scaling and multi-dimensional random inputs, Journal of Computational Physics, 462, 2022. Crossref

  2. Hellmuth Kathrin, Klingenberg Christian, Computing Black Scholes with Uncertain Volatility—A Machine Learning Approach, Mathematics, 10, 3, 2022. Crossref

  3. Medaglia Andrea, Tosin Andrea, Zanella Mattia, Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties, Partial Differential Equations and Applications, 3, 4, 2022. Crossref

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