New numerical studies for Darcy’s problem coupled with the heat equation

  • Dayana Dib
  • Séréna DibEmail author
  • Toni Sayah


In this article, we consider the heat equation coupled with Darcy’s law by a nonlinear viscosity depending on the temperature. We recall two numerical schemes and introduce a new non-stabilized one, we show the existence and uniqueness of the solutions and we establish an a priori error estimates using the Brezzi–Rappaz–Raviart theorem. Numerical investigations are preformed and showed.


Darcy’s equations Heat equation Brezzi–Rappaz–Raviart theorem Finite element method A priori error estimates 

Mathematics Subject Classification

35K05 35B45 74S05 76M10 



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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Laboratoire de Mathétiques et Applications, Unité de recherche Mathématiques et Modélisation, Faculté des SciencesUniversité Saint-JosephBeirutLebanon

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