Error analysis and convergence for the spectral synthesis method with interfaces

Abstract

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.