A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential. Exploiting the stability of the discretization, convergence is shown in the multi-dimensional case. Under some assumptions on the regularity of the solution, the rate of convergence proves to be optimal.
Mots-clés : higher order parabolic PDE, positivity, semidiscretization, stability, convergence, semiconductors
@article{M2AN_2003__37_2_277_0,
author = {J\"ungel, Ansgar and Pinnau, Ren\'e},
title = {Convergent semidiscretization of a nonlinear fourth order parabolic system},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {277--289},
publisher = {EDP-Sciences},
volume = {37},
number = {2},
year = {2003},
doi = {10.1051/m2an:2003026},
mrnumber = {1991201},
zbl = {1026.35045},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003026/}
}
TY - JOUR AU - Jüngel, Ansgar AU - Pinnau, René TI - Convergent semidiscretization of a nonlinear fourth order parabolic system JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 277 EP - 289 VL - 37 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003026/ DO - 10.1051/m2an:2003026 LA - en ID - M2AN_2003__37_2_277_0 ER -
%0 Journal Article %A Jüngel, Ansgar %A Pinnau, René %T Convergent semidiscretization of a nonlinear fourth order parabolic system %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 277-289 %V 37 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003026/ %R 10.1051/m2an:2003026 %G en %F M2AN_2003__37_2_277_0
Jüngel, Ansgar; Pinnau, René. Convergent semidiscretization of a nonlinear fourth order parabolic system. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 277-289. doi : 10.1051/m2an:2003026. http://archive.numdam.org/articles/10.1051/m2an:2003026/
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