Galerkin Spectral Synthesis Methods for Diffusion Equations with General Boundary Conditions
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Authors
Neta, Beny
Reich, Simeon
Victory, H. Dean Jr.
Subjects
Spectral synthesis
Neutron diffusion
Galerkin
Sobolev space
Neutron diffusion
Galerkin
Sobolev space
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Date of Issue
2002
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Abstract
An existence and uniqueness theory is developed for the energy dependent, steady state neutron diffusion equation with inhomogeneous oblique boundary conditions imposed. Also, a convergence theory is developed for the Galerkin Spectral Synthesis Approximations which arise when trial functions depending only on energy are utilized. The diffusion coefficient, the total and scattering cross-sectional data are all assumed to be both spatially and energy dependent. Interior interfaces defined by spatial discontinuities in the cross-section data are assumed present. Our estimates are in a Sobolev-type norm, and our results show that the spectral synthesis approximations are optimal in the sense of being of the same order as the error generated by the best approximation to the actual solution from the subspace to which the spectral synthesis approximations belong.
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Article
Description
Annals of Nuclear Energy, 29, (2002), 913–927.
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Department
Applied Mathematics
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.