Global Error Bounds for the Petrov-Galerkin Discretization of the Neutron Transport Equation [electronic resource].
- Washington, D.C. : United States. Dept. of Energy, 2005.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
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- PDF-file: 23 pages; size: 0.3 Mbytes
- Additional Creators:
- Lawrence Berkeley National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
- Restrictions on Access:
- Free-to-read Unrestricted online access
- In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L² norm at the rate of h². Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it takes a neutron to cross the domain in a straight line. A consequence of this bound is that the global error of the Petrov-Galerkin approximation is of the same order of h as the local truncation error. We use this result to explain the widely held observation that the solution of the Petrov-Galerkin method is second accurate for one class of problems, but is only first order accurate for another class of problems.
- Report Numbers:
- E 1.99:ucrl-proc-209167
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- Published through SciTech Connect.
Presented at: Nuclear Explosive Code Design Conference, Livermore , CA, United States, Oct 04 - Oct 07, 2004.
Brown, P; Chang, B; Greenbaum, A; Machorro, E.
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