Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system
ESAIM: Modélisation mathématique et analyse numérique, Volume 44 (2010) no. 3, pp. 573-595.

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 𝒪t2 + hmt), when the exact solution belongs to Hm.

DOI: 10.1051/m2an/2010012
Classification: 65M15, 65P40, 83C05
Keywords: Vlasov-Einstein system, semi-lagrangian methods, convergence analysis, general relativity
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     title = {Analysis of a semi-lagrangian method for the spherically symmetric {Vlasov-Einstein} system},
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Bechouche, Philippe; Besse, Nicolas. Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system. ESAIM: Modélisation mathématique et analyse numérique, Volume 44 (2010) no. 3, pp. 573-595. doi : 10.1051/m2an/2010012. http://www.numdam.org/articles/10.1051/m2an/2010012/

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