  In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme
for transport equations and applied it to kinetic simulations. The method uses
the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for
hyperbolic problems and is proven to be $L^2$ stable and convergent. A major
advantage of the scheme lies in its low computational and storage cost due to
the employed sparse finite element approximation space. This attractive feature
is explored in simulating Vlasov and Boltzmann transport equations. Good
performance in accuracy and conservation is verified by numerical tests in up
to four dimensions.
