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Zbl 1188.83010
Bechouche, Philippe; Besse, Nicolas
Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system. (English)
[J] ESAIM, Math. Model. Numer. Anal. 44, No. 3, 573-595 (2010). ISSN 0764-583X; ISSN 1290-3841/e

Summary: 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 $L^\infty$ and the statistical distribution function of the matter and its moments converge in $L^{2}$ with a rate of $\cal O (\Delta t^{2} + h^{m}/\Delta t)$, when the exact solution belongs to $H^{m}$.

MSC 2000:: *83C05 Einstein's equations
83C55 Hydrodynamics (general relativity)
65M15 Error bounds (IVP of PDE)
65P40 Nonlinear stabilities

Keywords: Vlasov-Einstein system; semi-Lagrangian methods; convergence analysis; general relativity

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Zentralblatt MATH Berlin [Germany]