Foundations of finite element applications to neutron transport

The use of finite elements in neutron transport gives deterministic treatments a geometrical capability with a flexibility comparable to that achievable by the stochastic Monte Carlo method. The principles used in obtaining solutions can be used also to assess the accuracy of numerical solutions. These assessment methods are illustrated by close bracketing bounds for local error and disadvantage factors. Principles are described for the steady state which guarantee neutron conservation for the whole finite element mesh. Some new principles are described which guarantee neutron conservation over each element of a mesh. For time dependent transport a principle guarantees neutron conservation with time over the whole mesh. The paper concludes with a sketch of fundamental work with the potential to exploit recent developments in computer architecture. (author)