  Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell
system, methods that are designed to be systematically as accurate as one wants
with provable conservation of mass and possibly total energy. Such properties
in general are hard to achieve within other numerical method frameworks for
simulating the Vlasov-Maxwell system. The proposed scheme employs discontinuous
Galerkin discretizations for both the Vlasov and the Maxwell equations,
resulting in a consistent description of the distribution function and
electromagnetic fields. It is proven, up to some boundary effects, that charge
is conserved and the total energy can be preserved with suitable choices of the
numerical flux for the Maxwell equations and the underlying approximation
spaces. Error estimates are established for several flux choices. The scheme is
tested on the streaming Weibel instability: the order of accuracy and
conservation properties of the proposed method are verified.
