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An Asymptotic Preserving Scheme for a Stochastic Linear Kinetic Equation in the Diffusion Regime

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From Particle Systems to Partial Differential Equations (ICPS 2019, ICPS 2018, ICPS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 352))

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Abstract

In this paper, we present an Asymptotic Preserving scheme for a stochastic linear kinetic equation. Its construction is based on a micro-macro decomposition. We start by explaining how we build it and then perform the formal numerical limit. After stating some stability results proved in [1], some numerical tests confirming the good performances of our scheme are finally presented.

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Authors and Affiliations

  1. Sorbonne Université, 4 place Jussieu, 75005, Paris, France

    Nathalie Ayi

Authors
  1. Nathalie Ayi
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Correspondence to Nathalie Ayi .

Editor information

Editors and Affiliations

  1. Laboratoire J.A. Dieudonné, UMR CNRS-UNS, Université Côte d’Azur, Nice Cedex 02, France

    Cédric Bernardin

  2. Centre de Math. Laurent Schwartz (CMLS), École Polytechnique, CMLS, Palaiseau Cedex, France

    François Golse

  3. Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    Patrícia Gonçalves

  4. Dipartimento di Matematica e Informatica, Università di Palermo, Palermo, Italy

    Valeria Ricci

  5. Centro de Matemática, Universidade do Minho, Braga, Portugal

    Ana Jacinta Soares

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Ayi, N. (2021). An Asymptotic Preserving Scheme for a Stochastic Linear Kinetic Equation in the Diffusion Regime. In: Bernardin, C., Golse, F., Gonçalves, P., Ricci, V., Soares, A.J. (eds) From Particle Systems to Partial Differential Equations. ICPS ICPS ICPS 2019 2018 2017. Springer Proceedings in Mathematics & Statistics, vol 352. Springer, Cham. https://doi.org/10.1007/978-3-030-69784-6_3

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