Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients. (English) Zbl 1460.65137
The paper is concerned with the numerical analysis of the multigroup neutron diffusion equation with piecewise polynomial coefficients on a rectangular 3D cuboid. The equation is considered either with an inhomogeneous term, or – mainly – as an eigenvalue problem. The problem is written in mixed form, and mixed finite element methods are applied, alternatively with or without (not necessarily matching) domain decomposition. Numerical experiments are carried out to illustrate the method.
Reviewer: Michael Plum (Karlsruhe)
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 |
| 82D75 | Nuclear reactor theory; neutron transport |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
diffusion equation; low-regularity solution; mixed formulation; eigenproblem; domain decomposition methodsReferences:
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