The rain on underground porous media Part I: Analysis of a richards model

Abstract

The Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler’s scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem.

Keywords

Richards equation / Porous media / Euler’s implicit scheme / Finite element discretization / Parabolic variational inequality

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