Nonlinear Equation of Unsteady Ground-Water Flow

A finite element weighted residual process has been used to solve nonlinear partial differential equations describing unsteady ground-water flows in an unconfined aquifer either into or out of a surface reservoir. Rectangular, as well as triangular, finite elements in a space-time solution domain were used. The weighting function was equal to the shape function defining the dependent variable approximation. The results are compared in dimensionless graphs with experimental as well as other numerical data. The finite element method compared favorably with these results and was found to be easily programmed, stable, computationally fast, rapidly convergent, and does not require constant parameters over the entire solution domain. This technique is another useful tool in solving field problems.