CPL - Chalmers Publication Library

# $L_p$ and eigenvalue error estimates for the discrete ordinates method for two-dimensional neutron transport

SIAM Journal on Numerical Analysis Vol. 26 (1989), 1, p. 66-87.

The convergence of the discrete ordinates method is studied for angular discretization of the neutron transport equation for a two-dimensional model problem with the constant total cross section and isotropic scattering. Considering a symmetric set of quadrature points on the unit circle, error estimates are derived for the scalar flux in $L_P$ norms for $1 \leqq p \leqq \infty$. A postprocessing procedure giving improved $L_\infty$ estimates is also analyzed. Finally error estimates are given for simple isolated eigenvalues of the solution operator.

Nyckelord: neutron transport equation, discrete ordinates method scalar flux, LP estimates, eigenvalue estimates, postprocessing, quadrature rule