an:01200912
Zbl 0918.65092
Asadzadeh, Mohammad
A finite element method for the neutron transport equation in an infinite cylindrical domain
EN
SIAM J. Numer. Anal. 35, No. 4, 1299-1314 (1998).
00051202
1998
j
65R20 45K05 82C70
neutron transport equation; spatial discretization; finite element; convergence rate; Besov spaces; interpolation spaces; scalar flux; duality algorithm; critical eigenvalue; error estimate
Author's abstract: We study the spatial discretization, in a fully discrete scheme, for the numerical solution of a model problem for the neutron transport equation in an infinite cylindrical domain. Based on using an interpolation technique in the discontinuous Galerkin finite element procedure, we derive an almost optimal error estimate for the scalar flux in the \(L_2\)-norm. Combining a duality argument applied to the above result with the previous semidiscrete error estimates for the velocity discretizations, we obtain globally optimal error bounds for the critical eigenvalues.
H.Brunner (St.John's)