Numerical approximation of an elliptic-parabolic equation arising in environment

Abstract.

We prove the convergence of a finite volume scheme for the Richards equation β(p)_t-div(λ(β(p)) (νp-ρg) =0, together with a Dirichlet boundary condition and an initial condition, in a bounded domain. We consider the hydraulic charge u=-z as the main unknown function so that no upwinding is necessary. The convergence proof is based on the strong convergence in L² of the water saturation β(p), which one obtains by estimating differences of space and time translates and applying Kolmogorov’s theorem.