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 formu-lation 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 irri-gation. 1