--- _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' ...