2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

Discontinuous Galerkin Schemes for Vlasov-Maxwell System

Yingda Cheng

Michigan State University

In this talk, we propose to use the discontinuous Galerkin (DG) methods to solve the Vlasov-Maxwell system. The scheme employs DG discretizations for both the Vlasov and the Maxwell's equations, resulting in a consistent description of the probability density function and electromagnetic fields. We prove that using this description the total particle numbers are conserved, and the total energy could be preserved upon a suitable choice of numerical flux for the Maxwell's equations and the underlying polynomial spaces on the semi-discrete level, if boundary effects can be neglected. We further established error estimates based on several flux choices. We test the scheme on the Weibel instability and verify the order and conservation of the method.