TY - JOUR

T1 - Efficient higher order nodal finite element formulations for neutron multigroup diffusion equations

AU - Hennart, J. P.

AU - Malambu Mbala, Edouard

AU - Mund, E. H.

AU - del Valle Gallegos, Edmundo

PY - 1996/9

Y1 - 1996/9

N2 - Several polynomial finite elements of nodal type are introduced that should lead to convergence of O(h3) in the L2 norm. Two of these methods are new and are expected to achieve the same orders of convergence with fewer parameters than the third method. They are applied to the one-group diffusion equation under different formulations, namely, several versions (with or without reduced and transverse integrations) of the primal and the mixed-hybrid formulations. Convergence rates are checked for a model problem with an analytical solution. Two of these methods exhibit superconvergence phenomena [O(h4) instead of O(h3)], a fact that can be explained heuristically. The most promising method, with only five parameters per cell, turns out to yield only O(h2) in its most algebraically efficient versions, while it has the potential of O(h3) convergence rates. Again, an explanation is given for this behavior and a fully O(h3) version is developed. Finally, these methods are applied to more realistic multigroup situations. In all cases, they are compared with results obtained from polynomial nodal methods in response matrix formalism. In the multigroup case, a well-known reference solution is also used.

AB - Several polynomial finite elements of nodal type are introduced that should lead to convergence of O(h3) in the L2 norm. Two of these methods are new and are expected to achieve the same orders of convergence with fewer parameters than the third method. They are applied to the one-group diffusion equation under different formulations, namely, several versions (with or without reduced and transverse integrations) of the primal and the mixed-hybrid formulations. Convergence rates are checked for a model problem with an analytical solution. Two of these methods exhibit superconvergence phenomena [O(h4) instead of O(h3)], a fact that can be explained heuristically. The most promising method, with only five parameters per cell, turns out to yield only O(h2) in its most algebraically efficient versions, while it has the potential of O(h3) convergence rates. Again, an explanation is given for this behavior and a fully O(h3) version is developed. Finally, these methods are applied to more realistic multigroup situations. In all cases, they are compared with results obtained from polynomial nodal methods in response matrix formalism. In the multigroup case, a well-known reference solution is also used.

KW - Calculations

KW - Diffusion

KW - Finite element method

KW - Polynomials

KW - Mathematical models

KW - Matrix algebra

KW - Integration

UR - http://www.scopus.com/inward/record.url?scp=0030246110&partnerID=8YFLogxK

U2 - 10.13182/NSE96-A24227

DO - 10.13182/NSE96-A24227

M3 - Article

AN - SCOPUS:0030246110

SN - 0029-5639

VL - 124

SP - 97

EP - 110

JO - Nuclear Science and Engineering

JF - Nuclear Science and Engineering

IS - 1

ER -