SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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An investigation of Strang and high order splitting schemes for Vlasov-type equations

L. Einkemmer and A. Ostermann

Abstract
In astro- and plasma physics the behavior of a collisionless plasma is modeled by the Vlasov equation coupled to an appropriate model of the electromagnetic field. For such a system Strang splitting is the most common integration method described in the literature. We provide a rigorous convergence analysis for the Strang splitting scheme in the case of Vlasov-type equations; this analysis is conducted in an abstract framework which includes the above mentioned applications. In addition, we show convergence of a full discretization for the electrostatic case, where this scheme is combined with a discontinuous Galerkin approximation in space. Due to the fact that the Strang splitting scheme, in general, is not symmetric, a straightforward extension to higher order methods, using composition, is not possible. To remedy this, we propose and analyze an explicit method which retains all favorable properties of the Strang splitting scheme.

Bibliography
[1] L. Einkemmer and A. Ostermann, Convergence analysis of Strang splitting for Vlasov-type equations, Preprint (arXiv:1207.2090), 2012.
[2] L. Einkemmer and A. Ostermann, Convergence analysis of a discontinuous Galerkin/Strang splitting approximation for the Vlasov-Poisson equations, Preprint (arXiv:1211.2353), 2012.
[3] L. Einkemmer and A. Ostermann, An almost symmetric Strang splitting scheme for the construction of high order composition methods, Preprint, 2013.

Organized by         Universidad de Valladolid     IMUVA