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 (Δt2 + hm/Δt), when the exact solution belongs to Hm.
@article{M2AN_2010__44_3_573_0,
author = {Bechouche, Philippe and Besse, Nicolas},
title = {Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {44},
year = {2010},
pages = {573-595},
doi = {10.1051/m2an/2010012},
mrnumber = {2666655},
zbl = {1188.83010},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2010__44_3_573_0}
}
Bechouche, Philippe; Besse, Nicolas. Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) pp. 573-595. doi : 10.1051/m2an/2010012. http://gdmltest.u-ga.fr/item/M2AN_2010__44_3_573_0/
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