Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations

Abstract

The Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson's equation, which rules the evolution of the self-consistent electric field. In this paper, we introduce a new class of forward Semi-Lagrangian schemes for the Vlasov-Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. The convergence in L1 norm of the schemes is proved and error estimates are obtained.

References in corpus (2)

• A Forward semi-Lagrangian Method for the Numerical Solution of the Vlasov Equation
• The remapped particle-mesh advection scheme

Cited by in corpus (7)

• Convergence analysis of Strang splitting for Vlasov-type equations
• A comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions
• Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov--Poisson equations
• Arbitrarily high order Convected Scheme solution of the Vlasov-Poisson system
• Arbitrary-order time-accurate semi-Lagrangian spectral approximations of the Vlasov-Poisson system
• High-order Hamiltonian splitting for Vlasov-Poisson equations
• Convergence of splitting methods on rotating grids for the magnetized Vlasov equation