A high-order artificial viscosity finite element method for the Vlasov-Poisson system

Abstract: We introduce a finite element method with high-order accuracy for approximating the Vlasov-Poisson system. This method uses continuous Lagrange polynomials as basis functions and employs explicit Runge-Kutta schemes for time discretization. A residual-based artificial viscosity technique is applied for stabilization. Numerical results show that this method is fourth-order accurate for smooth problems when using third-order polynomials combined with the fourth-order Runge-Kutta scheme. We explain the algorithms for obtaining the approximations of the electric field. The method is verified in the classic benchmark problems of the Vlasov-Poisson system, such as Landau damping, Two-stream instability, and Bump-on-tail instability in two-dimensional phase space.