--- _id: '9335' abstract: - lang: eng text: 'Various degenerate diffusion equations exhibit a waiting time phenomenon: depending on the “flatness” of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount of time. We show that this phenomenon is captured by particular Lagrangian discretizations of the porous medium and the thin film equations, and we obtain sufficient criteria for the occurrence of waiting times that are consistent with the known ones for the original PDEs. For the spatially discrete solution, the waiting time phenomenon refers to a deviation of the edge of support from its original position by a quantity comparable to the mesh width, over a mesh-independent time interval. Our proof is based on estimates on the fluid velocity in Lagrangian coordinates. Combining weighted entropy estimates with an iteration technique à la Stampacchia leads to upper bounds on free boundary propagation. Numerical simulations show that the phenomenon is already clearly visible for relatively coarse discretizations.' acknowledgement: This research was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics”. article_processing_charge: No article_type: original author: - first_name: Julian L full_name: Fischer, Julian L id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87 last_name: Fischer orcid: 0000-0002-0479-558X - first_name: Daniel full_name: Matthes, Daniel last_name: Matthes citation: ama: Fischer JL, Matthes D. The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. 2021;59(1):60-87. doi:10.1137/19M1300017 apa: Fischer, J. L., & Matthes, D. (2021). The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/19M1300017 chicago: Fischer, Julian L, and Daniel Matthes. “The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical Analysis. Society for Industrial and Applied Mathematics, 2021. https://doi.org/10.1137/19M1300017. ieee: J. L. Fischer and D. Matthes, “The waiting time phenomenon in spatially discretized porous medium and thin film equations,” SIAM Journal on Numerical Analysis, vol. 59, no. 1. Society for Industrial and Applied Mathematics, pp. 60–87, 2021. ista: Fischer JL, Matthes D. 2021. The waiting time phenomenon in spatially discretized porous medium and thin film equations. SIAM Journal on Numerical Analysis. 59(1), 60–87. mla: Fischer, Julian L., and Daniel Matthes. “The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations.” SIAM Journal on Numerical Analysis, vol. 59, no. 1, Society for Industrial and Applied Mathematics, 2021, pp. 60–87, doi:10.1137/19M1300017. short: J.L. Fischer, D. Matthes, SIAM Journal on Numerical Analysis 59 (2021) 60–87. date_created: 2021-04-18T22:01:42Z date_published: 2021-01-01T00:00:00Z date_updated: 2023-08-08T13:10:40Z day: '01' department: - _id: JuFi doi: 10.1137/19M1300017 external_id: arxiv: - '1911.04185' isi: - '000625044600003' intvolume: ' 59' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1911.04185 month: '01' oa: 1 oa_version: Preprint page: 60-87 publication: SIAM Journal on Numerical Analysis publication_identifier: issn: - 0036-1429 publication_status: published publisher: Society for Industrial and Applied Mathematics quality_controlled: '1' scopus_import: '1' status: public title: The waiting time phenomenon in spatially discretized porous medium and thin film equations type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 59 year: '2021' ...