Characteristic finite element method for the vlasov-poisson system

In particle simulation of plasmas, the initial positions and velocities of the particles are chosen according to the initial distribution function either randomly or in an ordered manner. The authors present the algorithm for the multidimensional Vlasov-Poisson system. The electrostatic energy calculated by the present method compares well with the particle simulation results up to a time of 10 plasma periods. Beyond this, the algorithm does not perform well due to the fine structure of f(t,x,v) as time increases. A suitable refinement of the present algorithm awaits further work