A priori error estimates for a mixed finite element discretization of the Richards’ equation

A mixed finite element discretization is applied to Richards’ equation, a nonlinear, possibly degenerate parabolic partial differential equation modeling water flow through porous medium. The equation is considered in its pressure formulation and includes both variably and fully saturated flow regime. Characteristic for such problems is the lack in regularity of the solution. To handle this we use a time-integrated scheme. We analyze the scheme and present error estimates showing its convergence.