# Convergent semidiscretization of a nonlinear fourth order parabolic system

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topJüngel, 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 -

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