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

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.