Computational aspects of FEM approximation of fractional advection dispersion equations on bounded domains in R2R2

In this paper, we investigate the numerical approximation of the variational solution to the fractional advection dispersion equation (FADE) on bounded domains in R2R2. More specifically, we investigate the computational aspects of the Galerkin approximation using continuous piecewise polynomial basis functions on a regular triangulation of the domain. The computational challenges of approximating the solution to fractional differential equations using the finite element method stem from the fact that a fractional differential operator is a non-local operator. Several numerical examples are given which demonstrate approximations to FADEs.