Comparison of finite element and global element methods in one-dimensional neutron diffusion

Determination of the neutron flux profile in a reactor is hampered by heterogeneities introduced by the fuel loading pattern and fuel burnup. The need for efficient computational techniques to solve for the spatial flux distribution has led to the application of several numerical approaches with varying degrees of success. The promise of the finite element method (FEM) has not materialized in the same way as the more favorable nodal methods. The purpose of this paper is to describe the application of a new variational technique, the global element method (GEM), to reactor analysis. The method was introduced by Delves and Hall and Delves and Phillips in the late 1970s. The GEM has several features that make it potentially attractive for analyzing heterogeneous cores using coarse meshes. As a means of assessing the usefulness of the method, this paper compares results for a test problem obtained using both the GEM and the FEM