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A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity

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Abstract

In this article, we study the time dependent Boussinesq (buoyancy) model with nonlinear viscosity depending on the temperature. We propose and analyze first and second order numerical schemes based on finite element methods. An optimal a priori error estimate is then derived for each numerical scheme. Numerical experiments are presented that confirm the theoretical accuracy of the discretization.

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Authors and Affiliations

  1. UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Sorbonne Universités, 75005, Paris, France

    Rim Aldbaissy & Frédéric Hecht

  2. Laboratoire de Mathétiques et Applications, Unité de recherche Mathématiques et Modélisation, Faculté des Sciences, Université Saint-Joseph, B.P 11-514, Riad El Solh, Beyrouth, 1107 2050, Lebanon

    Rim Aldbaissy, Gihane Mansour & Toni Sayah

Authors
  1. Rim Aldbaissy
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  2. Frédéric Hecht
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  3. Gihane Mansour
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  4. Toni Sayah
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Correspondence to Rim Aldbaissy.

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Aldbaissy, R., Hecht, F., Mansour, G. et al. A full discretisation of the time-dependent Boussinesq (buoyancy) model with nonlinear viscosity. Calcolo 55, 44 (2018). https://doi.org/10.1007/s10092-018-0285-0

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