Finite Element Solution of the Two-Dimensional Unsaturated Flow Equation,

摘要

The two-dimensional nonlinear partial differential equation describing the movement of groundwater is investigated using the finite element method. The relevant finite element theory is introduced using the two-dimensional linear diffusion equation and then applied to the unsaturated flow equation. The technique employed to solve the equation utilized isoparametric finite elements of the linear or quadratic type. The approach consists of expanding the nonlinear terms in shape functions and employing successive substitution until a fixed error criterion was satisfied. Convergence is usually very fast. Several examples are given comparing the results obtained to similar studies using finite difference techniques. A sample computer program is also provided. The theoretical questions of uniqueness and convergence are considered in detail and a rigorous derivation of error estimates is presented.