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- W2188406528 abstract "We derive error eatimates in certain weighted Lz-norms for the streamline diffu- sion and discontinuous Galerkin finite element methods for steady state, energy dependent, Fermi and Fokker-Plan& equations in two space dimensions, giving error bounds of order O(hkC'lz), for the weighted current function J, as in the convection dominated convection- diffusion problems, with J E H'+'(n) and h being the quasi-uniform meah size in triangu- lation of our three dimensional phase-space domain tl = I, x I, x I,, with z corresponding to the velocity variable. Our studies, in this paper, contain a priori error estimates for Fermi and Fokker-Planck equations with both piecewise continuous and piecewise discontinuous (in z and zy-directions) trial hnctiona. The malym are based on stability estimates which relay on an angular symmetry (not isotropy!) assumption. A continuation of this paper, the a posteriori error estimates for Fermi and Fokker-Plan& equations, is the subject of a future work. 0. Introduction. This is the first part in a series of two papers on the streamline diffusion finite element methods for degenerate type convection dominated convection- diffusion problems arise, e.g., in asymptotic expansion of particle transport for narrowly focussed pencil beams. In a pencil beam the mean direction change of beam particles is assumed to be small. This assumption, which is realistic for photon transport and certain electron transport problems is referred to as forward-peakedness of the scattering. Under certain assumptions, including strong forward-peakedness of the scattering, the transport equation can be well approximated by the Fokker-Planck equation. Formally, the equation is obtained by approximating the particle transport equation so that the scattering kernel associated with the total cross section give rise, after an asymptotic expansion, to a diffusion term with respect to the angular variable. The Fermi equation" @default.
- W2188406528 created "2016-06-24" @default.
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- W2188406528 date "1997-01-01" @default.
- W2188406528 modified "2023-09-27" @default.
- W2188406528 title "STREAMLINE DIFFUSION METHODS FOR FEW1 AND FOKKERPLANCK EQUATIONS" @default.
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