This talk will be divided in two parts. In the first, we will establish negative-order estimates for the accuracy of discontinuous Galerkin (DG) approximations to smooth solutions for the Vlasov-Maxwell (VM) system of equations. For the approximated solutions, we are able to extract this "hidden accuracy" through the use of a Smooth-Increasing Accuracy-Conserving (SIAC) filter which is a convolution kernel that is composed of a linear combination of B-splines. We provide rigorous error estimates for the DG solutions that show improvement to (2k + 1/2)-th order in the negative-order norm. In the second part we will analyze a hybrid method for radiation transport. The method that consists of (i) splitting the kinetic equation into collisional and non-collisional components; (ii) applying a high-order method to the non-collisional component and a low order method for the collisional component; and (iii) re-partitioning the kinetic distribution after each time step in the algorithm. In practice the hybrid method yields a more efficient method and provides a level of accuracy that is comparable to a uniform high-order treatment of the entire system. We provide for the first-time rigorous estimates for the hybrid method when we perform semi-discretization in angle in the collided component.