711
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A Priori Error Estimates and Computational Studies for a Fermi Pencil-Beam Equation

, , &

References

  • Adams, A. R. 1975. Sobolev spaces. New York, NY: Academic Press.
  • Asadzadeh, M., and A. Sopasakis. 2002. On fully discrete schemes for the Fermi pencil-beam equation. Comput. Methods Appl. Mech. Eng. 191 (1):4641–4659.
  • Asadzadeh, M., and E. Larsen. 2008. Linear transport equations in flatland with small angular diffusion and their finite element approximation. Math. Comput. Model (Elsevier). 47:495–514.
  • Asadzadeh, M. 1997. Streamline diffusion methods for Fermi and Fokker-Planck equations. Transport Theory Stat. Phys. 26 (3):319–340.
  • Asadzadeh, M. 2000. A posteriori error estimates for the Fokker-Planck and Fermi pencil beam equations. Math. Models Meth. Appl. Sci. 48,10 (5):737–769.
  • Asadzadeh, M. 2002. On the stability of characteristic schemes for the Fermi equation. Appl. Comput. Math. 1(1):158–174.
  • Borgers, C., and E. W. Larsen. 1996. Asymptotic derivation of the Fermi pencil-beam approximation. Nucl. Sci. Eng. 123:343–357.
  • Brenner, S. C., and L. R. Scott. 1994. The mathematical theory of finite element methods. Berlin: Springer-Verlag.
  • Ciarlet, P. G. 1941 [1980]. The finite element method for elliptic problems. New York, Oxford: Amsterdam North-Holland.
  • Eyges, L. 1948. Multiple scattering with energy loss. Phys. Rev. 74:1534–35.
  • Johnson, C. 1992. A new approach to algorithms for convection problems which are based on exact transport + projection. Comput. Methods Appl. Mech. Eng. 100:45–62.
  • Larsen, E. W., C. D. Levermore, G. C. Pomraning, and J. G. Sanderson. 1985. Discretization methods for one-dimensional Fokker-Planck operators. J. Comput. Phys. 61 (3):359–390.
  • Luo, Z.-M. and A. Brahme. 1993. An overview of the transport theory of charged particles. Radiat. Phys. Chem. 41:673.
  • Naqos, S. 2005. Numerical algorithms for electron beams. Master thesis, Chalmers University of Technology, Department of Mathematics.
  • Pomraning, G. C. 1992. The Fokker-Planck operator as an asymptotic limit. Math. Models Meth. Ap. Sci. 2:21.
  • Prinja, A. K., and G. C. Pomraning. 1996. One-dimensional beam transport. Transp. Theory Statist. Phys. 25 (2):231–247.
  • Rossi, B., and K. Greisen. 1941. Cosmic-ray theory. Rev. Mod. Phys. 13:265.