  We provide two new classes of moment models for linear kinetic equations in
slab and three-dimensional geometry. They are based on classical finite
elements and low-order discontinuous-Galerkin approximations on the unit
sphere. We investigate their realizability conditions and other basic
properties. Numerical tests show that these models are more efficient than
classical full-moment models in a space-homogeneous test, when the analytical
solution is not smooth.
