A numerical study of filtration problem in inhomogeneous dam with discontinuous permeability

  • Authors:

  • Abdelkrim Chakib;Touria Ghemires;Abdeljalil Nachaoui

  • Affiliations:

  • CNRS UMR 6629s Université de Nantes, BP 92208, F-44322 Nantes, France;Université Mohamed V, Faculté des Sciences, Département de Mathématiques de Informatique, B.P. 1014 Rabat, Morocco;CNRS UMR 6629s Université de Nantes, BP 92208, F-44322 Nantes, France

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2003

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Abstract

In this paper, we deal with an optimal shape design approach for the numerical realization of the flow problem of incompressible liquid through an inhomogeneous porous medium (say dam), with a class of permeability coefficients. Our interest is in studying numerical approximation of the solution of the optimal shape design problem proposed in [C. R. Acad. Sci. Paris Sér. I Math. 329 (10) (1999) 933-938]. We consider discretization of this problem based on linear finite elements. We prove the existence of the solution of the discrete problem. We study the convergence of the discrete problem. We present some results on numerical experiments including comparisons to the results obtained by a variational approach.