article published yes Jan Maas author 4C5696CE-F248-11E8-B48F-1D18A9856A870000-0002-0845-1338 Daniel Matthes author JaMa department 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. IOP Publishing2016 eng 1505.03178 00037886280000610.1088/0951-7715/29/7/1992 2971992 - 2023 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> 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, pp. 1992–2023, 2016. Maas J, Matthes D. 2016. Long-time behavior of a finite volume discretization for a fourth order diffusion equation. Nonlinearity. 29(7), 1992–2023. Maas, Jan, and Daniel Matthes. “Long-Time Behavior of a Finite Volume Discretization for a Fourth Order Diffusion Equation.” <i>Nonlinearity</i>. IOP Publishing, 2016. <a href="https://doi.org/10.1088/0951-7715/29/7/1992">https://doi.org/10.1088/0951-7715/29/7/1992</a>. 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, 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>. J. Maas, D. Matthes, Nonlinearity 29 (2016) 1992–2023. 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. <a href="https://doi.org/10.1088/0951-7715/29/7/1992">https://doi.org/10.1088/0951-7715/29/7/1992</a> 12612018-12-11T11:51:00Z2025-09-22T09:00:50Z