An adaptive method for characteristics-finite element method for solute transport equation in unsaturated porous media

An adaptive method for the solution of equation modeling the transport of solute by dispersion and advection in unsaturated porous media is presented. In many applications, when the peclet number is quite large, advection dominates diffusion and the concentration often develops sharp fronts. So finite elements are combined with the method of characteristics to treat this problem. Because a good approximation of velocities is necessary to calculate the advective term of the equation, the flow equation is approximated by parabolic mixed finite element method. An a posteriori error estimator is presented for adaptivity. This estimator yield upper and lower bounds on the error measured in the energy norm with constants which do not depend neither on meshsize nor on time step. Numerical examples presented here indicate that this method gives nearly exact approximations of sharp fronts.