Numerical solutions of nonlinear plasma equations by the finite-element method

Numerical solution of the nonlinear Vlasov's equation for a collisionless plasma by means of the finite-element Galerkin approximation is considered. An algorithm suitable for numerical calculations is proposed and explicit error estimates are given. Using these estimates, it is shown that the approximate solutions generated by the proposed algorithm converge to the true solution. Also the rate of convergence for the finite-element Galerkin approximation of the nonlinear Vlasov-Poisson equations is established. To gain some computational experience with the proposed algorithm, numerical experiments are performed for the case of a one-dimensional electron-ion plasma