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On fully discrete schemes for the Fermi pencil-beam equation

Asadzadeh, M. and Sopasakis, Alexandros LU (2002) In Computer Methods in Applied Mechanics and Engineering 191(41-42). p.4641-4659
Abstract
We consider a Fermi pencil-beam model in two-space dimensions (x,y), where x is aligned with the beam’s penetration direction and y together with the scaled angular variable z correspond to a, bounded symmetric, transversal cross-section. The model corresponds to a forward–backward degenerate, convection dominated, convection–diffusion problem. For this problem we study some fully discrete numerical schemes using the standard- and Petrov–Galerkin finite element methods, for discretizations of the transversal domain, combined with the backward Euler, Crank–Nicolson, and discontinuous Galerkin methods for discretizations in the penetration variable. We derive stability estimates for the semi-discrete problems. Further, assuming sufficiently... (More)
We consider a Fermi pencil-beam model in two-space dimensions (x,y), where x is aligned with the beam’s penetration direction and y together with the scaled angular variable z correspond to a, bounded symmetric, transversal cross-section. The model corresponds to a forward–backward degenerate, convection dominated, convection–diffusion problem. For this problem we study some fully discrete numerical schemes using the standard- and Petrov–Galerkin finite element methods, for discretizations of the transversal domain, combined with the backward Euler, Crank–Nicolson, and discontinuous Galerkin methods for discretizations in the penetration variable. We derive stability estimates for the semi-discrete problems. Further, assuming sufficiently smooth exact solution, we obtain optimal a priori error bounds in a triple norm. These estimates give rise to a priori error estimates in the L2-norm. Numerical implementations presented for some examples with the data approximating Dirac δ function, confirm the expected performance of the combined schemes. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Convergence rate, Fully discrete schemes, Semi-streamline diffusion, Standard Galerkin, Pencil beam, Fermi equation
in
Computer Methods in Applied Mechanics and Engineering
volume
191
issue
41-42
pages
4641 - 4659
publisher
Elsevier
external identifiers
  • scopus:0037073030
ISSN
0045-7825
DOI
10.1016/S0045-7825(02)00397-3
language
English
LU publication?
no
id
92c8d419-bf09-4429-a3b2-1693a3949be9 (old id 2201855)
date added to LUP
2012-01-01 17:45:50
date last changed
2017-01-01 04:42:30
@article{92c8d419-bf09-4429-a3b2-1693a3949be9,
  abstract     = {We consider a Fermi pencil-beam model in two-space dimensions (x,y), where x is aligned with the beam’s penetration direction and y together with the scaled angular variable z correspond to a, bounded symmetric, transversal cross-section. The model corresponds to a forward–backward degenerate, convection dominated, convection–diffusion problem. For this problem we study some fully discrete numerical schemes using the standard- and Petrov–Galerkin finite element methods, for discretizations of the transversal domain, combined with the backward Euler, Crank–Nicolson, and discontinuous Galerkin methods for discretizations in the penetration variable. We derive stability estimates for the semi-discrete problems. Further, assuming sufficiently smooth exact solution, we obtain optimal a priori error bounds in a triple norm. These estimates give rise to a priori error estimates in the L2-norm. Numerical implementations presented for some examples with the data approximating Dirac δ function, confirm the expected performance of the combined schemes.},
  author       = {Asadzadeh, M. and Sopasakis, Alexandros},
  issn         = {0045-7825},
  keyword      = {Convergence rate,Fully discrete schemes,Semi-streamline diffusion,Standard Galerkin,Pencil beam,Fermi equation},
  language     = {eng},
  number       = {41-42},
  pages        = {4641--4659},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {On fully discrete schemes for the Fermi pencil-beam equation},
  url          = {http://dx.doi.org/10.1016/S0045-7825(02)00397-3},
  volume       = {191},
  year         = {2002},
}