On convergence of FEM for the Fokker-Planck equation

Paper in proceeding, 1997

We give a priori error estimates in certain weighted $L_2$-norms for some finite element methods for steady state, energy dependent, Fermi and Fokker-Planck equations in two space dimensions, with the error bounds of order ${\Cal O}(h^{k+1/2})$, for the weighted current function $J\in H^{k+1}(\Omega)$ with $h$ being the quasi-uniform mesh size in triangulation of the three dimensional phase-space domain $\Omega =I_x\times I_y\times I_z$, where $z$ corresponding to the velocity variable.