A nonconforming finite element approximation of the transport equation in quadrangular and hexagonal geometries
(1996) Annals of Nuclear Energy — Vol. 23, n° 4-5, p. 285-300 (1996)
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- Abstract
- This paper introduces a new finite element approximation for multi-dimensional transport problems in piecewise homogeneous media. The transport equation is solved using a Galerkin technique with polynomial basis functions in space-angle variables derived from asymptotic transport theory. The phase space is partitioned into cells consistent with the geometry and having each an elemental expansion which is not a tensor product. improved accuracy may be obtained by multiplying the number of cells or/and increasing the polynomial degree. Numerical results on 1D and 2D reference problems in square geometry show a good agreement with other approximate methods.
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Citations
Devooght, J., Xing, H., & Mund, EH. (1996). A nonconforming finite element approximation of the transport equation in quadrangular and hexagonal geometries. Annals of Nuclear Energy, 23(4-5), 285-300. https://doi.org/10.1016/0306-4549(95)00099-2 (Original work published 1996)