Volume 44, Number 3, May-June 2010
|Page(s)||573 - 595|
|Published online||04 February 2010|
Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system
Departamento de Matemática Aplicada Facultad de Ciencias, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada, Spain. firstname.lastname@example.org
2 Institut de Mathématiques Elie Cartan & Institut Jean Lamour, Département Physique de la Matière et des Matériaux, Nancy-Université, Université Henri Poincaré, BP 70239, 54506 Vandœuvre-lès-Nancy Cedex, France. email@example.com
Revised: 7 September 2009
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.
Mathematics Subject Classification: 65M15 / 65P40 / 83C05
Key words: Vlasov-Einstein system / semi-Lagrangian methods / convergence analysis / general relativity
© EDP Sciences, SMAI, 2010
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