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 - <p style="text-align: justify;">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.</p>