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On fully discrete schemes for the Fermi pencil-beam equation

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Author

Summary, in English

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.

Publishing year

2002

Language

English

Pages

4641-4659

Publication/Series

Computer Methods in Applied Mechanics and Engineering

Volume

191

Issue

41-42

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Convergence rate
  • Fully discrete schemes
  • Semi-streamline diffusion
  • Standard Galerkin
  • Pencil beam
  • Fermi equation

Status

Published

ISBN/ISSN/Other

  • ISSN: 0045-7825