{"_id":"1261","language":[{"iso":"eng"}],"citation":{"short":"J. Maas, D. Matthes, Nonlinearity 29 (2016) 1992–2023.","ama":"Maas J, Matthes D. Long-time behavior of a finite volume discretization for a fourth order diffusion equation. <i>Nonlinearity</i>. 2016;29(7):1992-2023. doi:<a href=\"https://doi.org/10.1088/0951-7715/29/7/1992\">10.1088/0951-7715/29/7/1992</a>","apa":"Maas, J., &#38; Matthes, D. (2016). Long-time behavior of a finite volume discretization for a fourth order diffusion equation. <i>Nonlinearity</i>. IOP Publishing Ltd. <a href=\"https://doi.org/10.1088/0951-7715/29/7/1992\">https://doi.org/10.1088/0951-7715/29/7/1992</a>","chicago":"Maas, Jan, and Daniel Matthes. “Long-Time Behavior of a Finite Volume Discretization for a Fourth Order Diffusion Equation.” <i>Nonlinearity</i>. IOP Publishing Ltd., 2016. <a href=\"https://doi.org/10.1088/0951-7715/29/7/1992\">https://doi.org/10.1088/0951-7715/29/7/1992</a>.","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.","ieee":"J. Maas and D. Matthes, “Long-time behavior of a finite volume discretization for a fourth order diffusion equation,” <i>Nonlinearity</i>, vol. 29, no. 7. IOP Publishing Ltd., pp. 1992–2023, 2016.","mla":"Maas, Jan, and Daniel Matthes. “Long-Time Behavior of a Finite Volume Discretization for a Fourth Order Diffusion Equation.” <i>Nonlinearity</i>, vol. 29, no. 7, IOP Publishing Ltd., 2016, pp. 1992–2023, doi:<a href=\"https://doi.org/10.1088/0951-7715/29/7/1992\">10.1088/0951-7715/29/7/1992</a>."},"author":[{"full_name":"Maas, Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","last_name":"Maas","orcid":"0000-0002-0845-1338"},{"full_name":"Matthes, Daniel","last_name":"Matthes","first_name":"Daniel"}],"publication":"Nonlinearity","page":"1992 - 2023","doi":"10.1088/0951-7715/29/7/1992","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 ’ .","year":"2016","publist_id":"6062","volume":29,"intvolume":"        29","main_file_link":[{"url":"https://arxiv.org/abs/1505.03178","open_access":"1"}],"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."}],"department":[{"_id":"JaMa"}],"issue":"7","publication_status":"published","date_published":"2016-06-10T00:00:00Z","date_updated":"2021-01-12T06:49:28Z","month":"06","day":"10","type":"journal_article","status":"public","quality_controlled":"1","title":"Long-time behavior of a finite volume discretization for a fourth order diffusion equation","scopus_import":1,"publisher":"IOP Publishing Ltd.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:51:00Z","oa_version":"Preprint","oa":1}