Convergent semidiscretization of a nonlinear fourth order parabolic system

Ansgar Jüngel; René Pinnau

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 2, page 277-289
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Jüngel, Ansgar, and Pinnau, René. "Convergent semidiscretization of a nonlinear fourth order parabolic system." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 277-289. <http://eudml.org/doc/194163>.

@article{Jüngel2010,
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. },
author = {Jüngel, Ansgar, Pinnau, René},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Higher order parabolic PDE; positivity; semidiscretization; stability; convergence; semiconductors.; semiconductors; implicit time discretization; backward Euler scheme},
language = {eng},
month = {3},
number = {2},
pages = {277-289},
publisher = {EDP Sciences},
title = {Convergent semidiscretization of a nonlinear fourth order parabolic system},
url = {http://eudml.org/doc/194163},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Jüngel, Ansgar
AU - Pinnau, René
TI - Convergent semidiscretization of a nonlinear fourth order parabolic system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 277
EP - 289
AB - 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.
LA - eng
KW - Higher order parabolic PDE; positivity; semidiscretization; stability; convergence; semiconductors.; semiconductors; implicit time discretization; backward Euler scheme
UR - http://eudml.org/doc/194163
ER -

References

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