Numerical analysis of two-dimensional unsaturated soil water flow problems with two-grid finite element methods

In this paper, we investigate a two-grid finite element method (FEM) for two-dimensional nonlinear unsaturated soil water flow problems. The application of methods can transform the solution problems on fine grid to coarse and linear grid. Based error results standard FEM, derive continuous discrete time estimates in energy norm method. Numerical experiments are carried out with as an example illustrate that achieve similar optimal accuracy FEM less long two mesh sizes satisfy $ H = O(\sqrt{h}) $.