On Convergence of the Streamline Diffusion and Discontinuous Galerkin Methods for the Multi-Dimensional Fermi Pencil Beam Equation
Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 860–875
Abstract
We derive error estimates in the $L_2$ norms, for the streamline diffusion (SD) and discontinuous Galerkin (DG) 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. Here our focus is on theoretical aspects of the $h$ and $hp$ approximations in both SD and DG settings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-600
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 860–875
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Fermi equation particle beam streamline diffusion discontinuous Galerkin stability convergence.