Geodesic
Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 3, pp. 573-595

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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.

DOI : 10.1051/m2an/2010012
Classification : 65M15, 65P40, 83C05
Keywords: Vlasov-Einstein system, semi-lagrangian methods, convergence analysis, general relativity 
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     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 },
     pages = {573--595},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {3},
     year = {2010},
     doi = {10.1051/m2an/2010012},
     mrnumber = {2666655},
     zbl = {1188.83010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010012/}
}
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Bechouche, Philippe; Besse, Nicolas. Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 3, pp. 573-595. doi: 10.1051/m2an/2010012

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