  In this paper, we introduce second order and fourth order space
discretization via finite difference implementation of the finite element
method for solving Fokker-Planck equations associated with irreversible
processes. The proposed schemes are first order in time and second order and
fourth order in space. Under mild mesh conditions and time step constraints for
smooth solutions, the schemes are proved to be monotone, thus are
positivity-preserving and energy dissipative. In particular, our scheme is
suitable for capturing steady state solutions in large final time simulations.
