Abstract: A numerical scheme for the Fokker-Planck equation is proposed with a finite element method,which is relatively simple for implementation and physically clear. It assures a positive distribution function and particle-number conservation without specific requirement on grid and time step.The scheme is confirmed in one-dimensional simulations.It can be extended easily to multi-dimensional cases.

Key words: Fokker-Planck equation, finite element method, plasmas, Legendre series