%0 Journal Article
%T The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Kazemi, E.
%D 2013
%\ 12/15/2013
%V 39
%N 6
%P 1159-1180
%! The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation
%K Fermi equation
%K particle beam
%K streamline diffusion
%K Backward Euler
%K Stability
%K convergence
%R
%X We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent in the sense that the time derivative is includedin the stabilization term. Here our focus is on theoretical aspects of the h andhp approximations in SD settings.
%U http://bims.iranjournals.ir/article_467_6a62e34662811d8fa55d39ce9ae949e3.pdf