Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
A finite element code for the simulation of one-dimensional Vlasov plasmas I. Theory
Journal of Computational Physics
A finite element code for the simulation of one-dimensional Vlasov plasmas. II.Applications
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Journal of Computational Physics
A splitting algorithm for Vlasov simulation with filamentation filtration
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
Numerical study on Landau damping
Physica D
Conservative numerical schemes for the Vlasov equation
Journal of Computational Physics
Plasma Physics Via Computer
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A discontinuous Galerkin method for the Vlasov-Poisson system
Journal of Computational Physics
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
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In this paper we consider Runge---Kutta discontinuous Galerkin (RKDG) schemes for Vlasov---Poisson systems that model collisionless plasmas. One-dimensional systems are emphasized. The RKDG method, originally devised to solve conservation laws, is seen to have excellent conservation properties, be readily designed for arbitrary order of accuracy, and capable of being used with a positivity-preserving limiter that guarantees positivity of the distribution functions. The RKDG solver for the Vlasov equation is the main focus, while the electric field is obtained through the classical representation by Green's function for the Poisson equation. A rigorous study of recurrence of the DG methods is presented by Fourier analysis, and the impact of different polynomial spaces and the positivity-preserving limiters on the quality of the solutions is ascertained. Several benchmark test problems, such as Landau damping, the two-stream instability, and the Kinetic Electro static Electron Nonlinear wave, are given.