On fully discrete schemes for the Fermi pencilbeam equation
(2002) In Computer Methods in Applied Mechanics and Engineering 191(4142). p.46414659 Abstract
 We consider a Fermi pencilbeam model in twospace 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 crosssection. 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 semidiscrete problems. Further, assuming sufficiently... (More)
 We consider a Fermi pencilbeam model in twospace 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 crosssection. 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 semidiscrete 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 L2norm. Numerical implementations presented for some examples with the data approximating Dirac δ function, confirm the expected performance of the combined schemes. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2201855
 author
 Asadzadeh, M. and Sopasakis, Alexandros ^{LU}
 publishing date
 2002
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Convergence rate, Fully discrete schemes, Semistreamline diffusion, Standard Galerkin, Pencil beam, Fermi equation
 in
 Computer Methods in Applied Mechanics and Engineering
 volume
 191
 issue
 4142
 pages
 4641  4659
 publisher
 Elsevier
 external identifiers

 scopus:0037073030
 ISSN
 00457825
 DOI
 10.1016/S00457825(02)003973
 language
 English
 LU publication?
 no
 id
 92c8d419bf094429a3b21693a3949be9 (old id 2201855)
 date added to LUP
 20120101 17:45:50
 date last changed
 20180107 05:36:34
@article{92c8d419bf094429a3b21693a3949be9, abstract = {We consider a Fermi pencilbeam model in twospace 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 crosssection. 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 semidiscrete 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 L2norm. 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 = {00457825}, keyword = {Convergence rate,Fully discrete schemes,Semistreamline diffusion,Standard Galerkin,Pencil beam,Fermi equation}, language = {eng}, number = {4142}, pages = {46414659}, publisher = {Elsevier}, series = {Computer Methods in Applied Mechanics and Engineering}, title = {On fully discrete schemes for the Fermi pencilbeam equation}, url = {http://dx.doi.org/10.1016/S00457825(02)003973}, volume = {191}, year = {2002}, }