Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system

Philippe Bechouche; Nicolas Besse

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 3, page 573-595
  • ISSN: 0764-583X

Abstract

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We consider the spherically symmetric Vlasov-Einstein system in the case of asymptotically flat spacetimes. From the physical point of view this system of equations can model the formation of a spherical black hole by gravitational collapse or describe the evolution of galaxies and globular clusters. We present high-order numerical schemes based on semi-Lagrangian techniques. The convergence of the solution of the discretized problem to the exact solution is proven and high-order error estimates are supplied. More precisely the metric coefficients converge in L∞ and the statistical distribution function of the matter and its moments converge in L2 with a rate of 𝒪 (Δt2 + hm/Δt), when the exact solution belongs to Hm.

How to cite

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Bechouche, Philippe, and Besse, Nicolas. "Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system." ESAIM: Mathematical Modelling and Numerical Analysis 44.3 (2010): 573-595. <http://eudml.org/doc/250818>.

@article{Bechouche2010,
abstract = { We consider the spherically symmetric Vlasov-Einstein system in the case of asymptotically flat spacetimes. From the physical point of view this system of equations can model the formation of a spherical black hole by gravitational collapse or describe the evolution of galaxies and globular clusters. We present high-order numerical schemes based on semi-Lagrangian techniques. The convergence of the solution of the discretized problem to the exact solution is proven and high-order error estimates are supplied. More precisely the metric coefficients converge in L∞ and the statistical distribution function of the matter and its moments converge in L2 with a rate of $\mathcal\{O\}$ (Δt2 + hm/Δt), when the exact solution belongs to Hm. },
author = {Bechouche, Philippe, Besse, Nicolas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Vlasov-Einstein system; semi-Lagrangian methods; convergence analysis; general relativity},
language = {eng},
month = {4},
number = {3},
pages = {573-595},
publisher = {EDP Sciences},
title = {Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system},
url = {http://eudml.org/doc/250818},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Bechouche, Philippe
AU - Besse, Nicolas
TI - Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/4//
PB - EDP Sciences
VL - 44
IS - 3
SP - 573
EP - 595
AB - We consider the spherically symmetric Vlasov-Einstein system in the case of asymptotically flat spacetimes. From the physical point of view this system of equations can model the formation of a spherical black hole by gravitational collapse or describe the evolution of galaxies and globular clusters. We present high-order numerical schemes based on semi-Lagrangian techniques. The convergence of the solution of the discretized problem to the exact solution is proven and high-order error estimates are supplied. More precisely the metric coefficients converge in L∞ and the statistical distribution function of the matter and its moments converge in L2 with a rate of $\mathcal{O}$ (Δt2 + hm/Δt), when the exact solution belongs to Hm.
LA - eng
KW - Vlasov-Einstein system; semi-Lagrangian methods; convergence analysis; general relativity
UR - http://eudml.org/doc/250818
ER -

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