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Convergent semidiscretization of a nonlinear fourth order parabolic system

Published online by Cambridge University Press:  15 November 2003

Ansgar Jüngel  and
René Pinnau
Ansgar Jüngel
Affiliation:
Fachbereich Mathematik, Universität Konstanz, 78457 Konstanz, Germany. juengel@mathematik.uni-konstanz.de.
René Pinnau
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, 64289 Darmstadt, Germany. pinnau@mathematik.tu-darmstadt.de.
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Abstract

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.

Keywords

Higher order parabolic PDEpositivitysemidiscretizationstabilityconvergencesemiconductors.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 2 , March 2003 , pp. 277 - 289
Copyright
© EDP Sciences, SMAI, 2003

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