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Journal Articles Numerische Mathematik Year : 2018

Finite element methods for Darcy’s problem coupled with the heat equation

Christine Bernardi
  • Function : Author
Séréna Dib
  • Function : Author
Vivette Girault
  • Function : Author
Frédéric Hecht
  • Function : Author
François Murat
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Toni Sayah
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Abstract

In this article, we study theoretically and numerically the heat equation coupled with Darcy’s law by a nonlinear viscosity depending on the temperature. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We propose and analyze two 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. ------------------------- This paper has been published in Numer. Math., 139, (2018), pp. 315-348, doi 10.1007/s00211-017-0938-y
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Dates and versions

hal-03878535 , version 1 (29-11-2022)

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Christine Bernardi, Séréna Dib, Vivette Girault, Frédéric Hecht, François Murat, et al.. Finite element methods for Darcy’s problem coupled with the heat equation. Numerische Mathematik, 2018, 139 (2), pp.315-348. ⟨10.1007/s00211-017-0938-y⟩. ⟨hal-03878535⟩
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