The Galerkin Method for nonlinear parabolic equations of unsteady groundwater flow

This paper suggests a relatively simple way for solving nonlinear parabolic partial differential equations associated with unsteady groundwater flow. The Galerkin formulation is discretized in the space domain by using piecewise polynomial equations, and the trapezoidal formula is employed to approximate the time derivative. The resulting system of nonlinear equations is then solved by the Newton method. Rapid rate of convergence and easy computer implementation are demonstrated by numerical examples. Results compare favorably with published experimental data.