A Finite‐Element Collocation Method for Variably Saturated Flow in Two Space Dimensions

This paper introduces a finite‐element collocation technique for solving the equation governing two‐dimensional flow in a variably saturated porous medium. The scheme uses a mass‐conserving formulation of Richards' equation as the basis for the finite‐difference time‐stepping method. Collocation in tensor‐product spaces of Hermite cubics yields a computationally efficient finite‐element approximation of the spatial derivatives. A Newton‐like iteration gives a temporally stable implicit scheme. The paper examines two sample problems, including an initial boundary‐value problem involving subsurface irrigation.