Finite element error expansions for the eigenvalue approximation to the multigroup diffusion equations. (English) Zbl 0783.65073
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.
Reviewer: P.Burda (Praha)
MSC:
65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |
35P15 | Estimates of eigenvalues in context of PDEs |