Abstract:
We discuss a mathematical model arising in the filtration of a
fluid through a porous medium. The model leads to a free boundary
value problem whose governing equation depends on the retention
function. A numerical approximation by means of finite elements
is used to present an existence and uniqueness theorem along with
an error estimate for a linear retention function. Finally, numerical algorithms for finding approximate solutions for linear and quadratic retention functions are suggested and the results of
numerical calculations are given.
