Volume 10, Issue 4
On Convergence of the Streamline Diffusion and Discontinuous Galerkin Methods for the Multi-Dimensional Fermi Pencil Beam Equation

Int. J. Numer. Anal. Mod., 10 (2013), pp. 860-875.

Published online: 2013-10

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• 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.

• Keywords

Fermi equation, particle beam, streamline diffusion, discontinuous Galerkin, stability, convergence.

65M15 65M60

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@Article{IJNAM-10-860, author = {}, title = {On Convergence of the Streamline Diffusion and Discontinuous Galerkin Methods for the Multi-Dimensional Fermi Pencil Beam Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/600.html} }
TY - JOUR T1 - On Convergence of the Streamline Diffusion and Discontinuous Galerkin Methods for the Multi-Dimensional Fermi Pencil Beam Equation JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 860 EP - 875 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/600.html KW - Fermi equation, particle beam, streamline diffusion, discontinuous Galerkin, stability, convergence. AB -

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.

M. Asadzadeh & E. Kazemi. (1970). On Convergence of the Streamline Diffusion and Discontinuous Galerkin Methods for the Multi-Dimensional Fermi Pencil Beam Equation. International Journal of Numerical Analysis and Modeling. 10 (4). 860-875. doi:
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