Discontinuous finite element solutions for neutron transport in x-y geometry

A finite element method of composit solutions is described for the even-parity transport equation which uses a high order spherical harmonic expansions for the directional component of transport where they are needed and not everywhere as in established finite element methods. Previously in the method of composite solution trial functions were needed for both even and o.dd parity angular fluxes. For some problems there is a small saving in the number of unknowns used to specify a variational solution but for others savings of the order I)f 70% can be achived. The method is illustrated by numerical solutio!1s in two dimensions for a Fletcher test problem, a PWR cell problem of Natelson and a problem of a quarter of a reactor with three control rods.