The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation

Document Type : Research Paper


Isfahan University of Technology, Isfahan, Iran


We derive error estimates in the appropriate norms, for the streamline
diffusion (SD) finite element methods for steady state, energy dependent,
Fermi equation in three space dimensions. These estimates yield optimal convergence
rates due to the maximal available regularity of the exact solution.
High order SD method together with implicit integration are used. The formulation
is strongly consistent in the sense that the time derivative is included
in the stabilization term. Here our focus is on theoretical aspects of the h and
hp approximations in SD settings.


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