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

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

neutron transport equation

discrete ordinates method scalar flux

LP estimates

eigenvalue estimates

postprocessing

quadrature rule

LP estimates

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