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A finite element method for the neutron transport equation in an infinite cylindrical domain. (English) Zbl 0918.65092
Author’s abstract: We study the spatial discretization, in a fully discrete scheme, for the numerical solution of a model problem for the neutron transport equation in an infinite cylindrical domain. Based on using an interpolation technique in the discontinuous Galerkin finite element procedure, we derive an almost optimal error estimate for the scalar flux in the \(L_2\)-norm. Combining a duality argument applied to the above result with the previous semidiscrete error estimates for the velocity discretizations, we obtain globally optimal error bounds for the critical eigenvalues.

MSC:
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
82C70 Transport processes in time-dependent statistical mechanics
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