Convergence analysis for a mixed finite element scheme for flow in strictly unsaturated porous media

Abstract

In this paper, we analyze a fully discrete numerical scheme for water flow in strictly unsaturated porous media. The water flow is modeled by the Richards equation, a nonlinear parabolic partial differential equation. The scheme is based on the Euler implicit (EI) for the discretization in time, and the mixed finite element method (MFEM), more precisely the lowest order Raviart–Thomas elements, for the discretization in space. Error estimates are derived to show the convergence of the scheme. An optimal order of convergence is obtained. The paper concludes with two numerical tests, which are in good agreement with the theoretical estimates.