  The numerical solution of a nonlinear and space-fractional anti-diffusive
equation used to model dune morphodynamics is considered. Spatial
discretization is effected using a finite element method whereas the
Crank-Nicolson scheme is used for temporal discretization. The fully discrete
scheme is analyzed to determine stability condition and also to obtain error
estimates for the approximate solution. Numerical examples are presented to
illustrate convergence results.
