Enhanced Convergence Estimates for Semi-Lagrangian Schemes Application to the Vlasov--Poisson Equation
نویسندگان
چکیده
منابع مشابه
Enhanced Convergence Estimates for Semi-Lagrangian Schemes Application to the Vlasov-Poisson Equation
We prove enhanced error estimates for high order semi-lagrangian discretizations of the Vlasov-Poisson equation. It provides new insights into optimal numerical strategies for the numerical solution of this problem. The new error estimate O ( min ( ∆x ∆t , 1 ) ∆x + ∆t ) is based on advanced error estimates for semi-lagrangian schemes, also equal to shifted Strang’s schemes, for the discretizati...
متن کاملConvergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system
In this paper we present some classes of high-order semi-Lagrangian schemes for solving the periodic one-dimensional Vlasov-Poisson system in phase-space on uniform grids. We prove that the distribution function f(t, x, v) and the electric field E(t, x) converge in the L2 norm with a rate of O ( ∆t + h + hm+1 ∆t ) , where m is the degree of the polynomial reconstruction, and ∆t and h are respec...
متن کاملConservative semi-Lagrangian schemes for Vlasov equations
Conservative methods for the numerical solution of the Vlasov equation are developed in the context of the one-dimensional splitting. In the case of constant advection, these methods and the traditional semi-Lagrangian ones are proven to be equivalent, but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity. In the non constant advection case...
متن کاملOn the geometric properties of the semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equation
The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov–Poisson equation. Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes. In this paper we study the conservation of important invari...
متن کاملAnalysis of a new class of forward semi-Lagrangian schemes for the 1D Vlasov Poisson equations
The Vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles. It is self-consistently coupled with Poisson’s equation, which rules the evolution of the 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 nume...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2013
ISSN: 0036-1429,1095-7170
DOI: 10.1137/110851511