Summary
Error estimates and convergence are studied for the Galerkin-type spectral synthesis method relative to the continuous-energy, continuous-space, time-independent neutron diffusion equation. The diffusion coefficient and total macroscopic cross section are both space and energy dependent, and interfaces may be present. The estimate is in an energy type norm. The basic result shows that the error is optimal in the sense of being of the same order as the error provided by the best approximation to the actual solution in the approximation space where the spectral synthesis solution is found.
Zusammenfassung
Fehlerabschätzung und Konvergenz der Galerkin-ähnlichen Spektralsynthesenmethode, angewandt auf die zeitunabhängige Neutronendiffusionsgleichung mit kontinuierlicher Abhängigkeit von Ort und Energie, werden diskutiert. Der Diffusionskoeffizient und der makroskopische Gesamtquerschnitt hängen beide von Ort und Energie ab, wobei auch Zwischengrenzen möglich sind. Die Fehlerschätzung erfolgt in einer Energietypennorm. Das Grundergebnis zeigt, dass der Fehler optimal ist in dem Sinne, dass er von der gleichen Ordnung ist wie der Fehler entstanden durch die beste Näherung zur exakten Lösung im Approximationenraum, wo die Spektralsynthesenlösung gefunden wird.
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This research was partially supported by the U.S. National Science Foundation under grant No. ENG77-06766.
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Meyer, H.D., Nelson, P. Error analysis and convergence for the spectral synthesis method with interfaces. Journal of Applied Mathematics and Physics (ZAMP) 30, 901–912 (1979). https://doi.org/10.1007/BF01590488
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DOI: https://doi.org/10.1007/BF01590488