Authors’ abstract: Asymptotic expansions for the finite element approximation to the eigenvalues of multigroup diffusion equations from reactor theory on \(2D\) or \(3D\) domains are given, first for a piecewise uniform triangulation, then for nonuniform quadrilateral meshes, and finally for nonuniform hexahedral meshes. The effect of numerical integration is studied. Extrapolation formulas and error estimates are obtained.