| Issue |
ESAIM: M2AN
Volume 37, Number 2, March/April 2003
|
|
|---|---|---|
| Page(s) | 277 - 289 | |
| DOI | https://doi.org/10.1051/m2an:2003026 | |
| Published online | 15 November 2003 | |
Convergent semidiscretization of a nonlinear fourth order parabolic system
1
Fachbereich Mathematik, Universität Konstanz, 78457 Konstanz, Germany. juengel@mathematik.uni-konstanz.de.
2
Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany. pinnau@mathematik.tu-darmstadt.de.
Received:
29
May
2002
Revised:
20
November
2002
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.
Mathematics Subject Classification: 35K35 / 65M12 / 65M15 / 65M20 / 76Y05
Key words: Higher order parabolic PDE / positivity / semidiscretization / stability / convergence / semiconductors.
© EDP Sciences, SMAI, 2003
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