On Fully Discrete Schemes for the Fermi Pencil-Beam Equations.
Journal article, 2002

We consider standard Galerkin and streamline diffusion finite element methods in the two dimensional, bounded transversal domain combined with backward Euler, Crank-Nicolson and discontinuous Galerkin methods in the penetration variable. Assuming smooth solutions in the Sobolev space $H^{k+1}$ of functions with their partial derivatives up to order $k+1$ in $L_2$, we derive optimal, a priori, semi-discrete methods of order $O(h^k)$ and $O(h^{k+1/2})$, respectively. Numerical implementations are presented


Standard Galerkin

Fermi equation

Pencil beam

Fully discrete scheme

Convergence rates


Mohammad Asadzadeh

Chalmers, Department of Mathematics

University of Gothenburg

Alexandros Sopasakis

Chalmers, Department of Mathematics

University of Gothenburg

Computer Methods in Applied Mechanics and Engineering

0045-7825 (ISSN)

Vol. 191 41-42 4641-4659

Subject Categories

Computational Mathematics

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