---
_id: '1261'
abstract:
- lang: eng
text: 'We consider a non-standard finite-volume discretization of a strongly non-linear
fourth order diffusion equation on the d-dimensional cube, for arbitrary . The
scheme preserves two important structural properties of the equation: the first
is the interpretation as a gradient flow in a mass transportation metric, and
the second is an intimate relation to a linear Fokker-Planck equation. Thanks
to these structural properties, the scheme possesses two discrete Lyapunov functionals.
These functionals approximate the entropy and the Fisher information, respectively,
and their dissipation rates converge to the optimal ones in the discrete-to-continuous
limit. Using the dissipation, we derive estimates on the long-time asymptotics
of the discrete solutions. Finally, we present results from numerical experiments
which indicate that our discretization is able to capture significant features
of the complex original dynamics, even with a rather coarse spatial resolution.'
acknowledgement: This research was supported by the DFG Collaborative Research Centers TRR 109, ‘
Discretization in Geometry and Dynamics ’ and 1060 ‘ The Mathematics of Emergent
Effects ’ .
author:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Daniel
full_name: Matthes, Daniel
last_name: Matthes
citation:
ama: Maas J, Matthes D. Long-time behavior of a finite volume discretization for
a fourth order diffusion equation. Nonlinearity. 2016;29(7):1992-2023.
doi:10.1088/0951-7715/29/7/1992
apa: Maas, J., & Matthes, D. (2016). Long-time behavior of a finite volume discretization
for a fourth order diffusion equation. Nonlinearity. IOP Publishing Ltd.
https://doi.org/10.1088/0951-7715/29/7/1992
chicago: Maas, Jan, and Daniel Matthes. “Long-Time Behavior of a Finite Volume Discretization
for a Fourth Order Diffusion Equation.” Nonlinearity. IOP Publishing Ltd.,
2016. https://doi.org/10.1088/0951-7715/29/7/1992.
ieee: J. Maas and D. Matthes, “Long-time behavior of a finite volume discretization
for a fourth order diffusion equation,” Nonlinearity, vol. 29, no. 7. IOP
Publishing Ltd., pp. 1992–2023, 2016.
ista: Maas J, Matthes D. 2016. Long-time behavior of a finite volume discretization
for a fourth order diffusion equation. Nonlinearity. 29(7), 1992–2023.
mla: Maas, Jan, and Daniel Matthes. “Long-Time Behavior of a Finite Volume Discretization
for a Fourth Order Diffusion Equation.” Nonlinearity, vol. 29, no. 7, IOP
Publishing Ltd., 2016, pp. 1992–2023, doi:10.1088/0951-7715/29/7/1992.
short: J. Maas, D. Matthes, Nonlinearity 29 (2016) 1992–2023.
date_created: 2018-12-11T11:51:00Z
date_published: 2016-06-10T00:00:00Z
date_updated: 2021-01-12T06:49:28Z
day: '10'
department:
- _id: JaMa
doi: 10.1088/0951-7715/29/7/1992
intvolume: ' 29'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1505.03178
month: '06'
oa: 1
oa_version: Preprint
page: 1992 - 2023
publication: Nonlinearity
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '6062'
quality_controlled: '1'
scopus_import: 1
status: public
title: Long-time behavior of a finite volume discretization for a fourth order diffusion
equation
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2016'
...