, Volume 53, Issue 4, pp 659–690

Spectral discretization of an unsteady flow through a porous solid



We consider the non stationary flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the problem is nonlinear. We propose a discretization of this equation that combines Euler’s implicit scheme in time and spectral methods in space. We prove optimal a priori error estimates and present some numerical experiments which confirm the interest of the discretization.


Darcy’s equations Time discretization Spectral method 

Mathematics Subject Classification

35B45 65M70 65N35 76S05 


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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  • Christine Bernardi
    • 1
  • Sarra Maarouf
    • 1
  • Driss Yakoubi
    • 2
  1. 1.Laboratoire Jacques-Louis LionsC.N.R.S. & Université Pierre et Marie CurieParis Cedex 05France
  2. 2.GIREF, Département de Mathématiques et de Statistique, Pavillon VachonUniversité de LavalQuébecCanada

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