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.
Keywords: Vlasov-Einstein system, semi-lagrangian methods, convergence analysis, general relativity
@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: Mod\'elisation math\'ematique et analyse num\'erique}, 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://www.numdam.org/articles/10.1051/m2an/2010012/} }
TY - JOUR AU - Bechouche, Philippe AU - Besse, Nicolas TI - Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 573 EP - 595 VL - 44 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010012/ DO - 10.1051/m2an/2010012 LA - en ID - M2AN_2010__44_3_573_0 ER -
%0 Journal Article %A Bechouche, Philippe %A Besse, Nicolas %T Analysis of a semi-lagrangian method for the spherically symmetric Vlasov-Einstein system %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 573-595 %V 44 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010012/ %R 10.1051/m2an/2010012 %G en %F M2AN_2010__44_3_573_0
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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