Convergence of a particle-in-cell scheme for the spherically symmetric Vlasov-Einstein system

Details Convergence of a particle-in-cell scheme for the spherically symmetric Vlasov-Einstein system Convergence of a particle-in-cell scheme for the spherically symmetric Vlasov-Einstein system

2002-09-25

arxiv.org/abs/math/0209336v1

Indiana Univ. Math. Journal, Vol. 52, No. 4, 821-861 (2003)

Mathematics

Numerical Analysis

38 pages

Scientific paper

We consider spherically symmetric, asymptotically flat space-times with a collisionless gas as matter model. Many properties of the resulting Vlasov-Einstein system are not yet accessible by purely analytical means. We present a discretized version of this system which is suitable for numerical implementation and is based on the particle-in-cell technique. Convergence of the resulting approximate solutions to the exact solution is proven and error bounds are provided.

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