eprintid: 1476860 rev_number: 23 eprint_status: archive userid: 608 dir: disk0/01/47/68/60 datestamp: 2016-03-21 10:30:44 lastmod: 2021-12-18 23:57:57 status_changed: 2016-03-21 10:30:44 type: article metadata_visibility: show creators_name: Burman, E title: A monotonicity preserving, nonlinear, finite element upwind method for the transport equation ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F59 keywords: Stabilized finite element method; Shock capturing; Flux correction; Monotonicity preserving; Transport equation note: © 2015. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licences are available at http://creativecommons.org/licenses/by/4.0. abstract: We propose a simple upwind finite element method that is monotonicity preserving and weakly consistent of order O(h3/2). The scheme is nonlinear, but since an explicit time integration method is used the added cost due to the nonlinearity is not prohibitive. We prove the monotonicity preserving property for the forward Euler method and for a second order Runge–Kutta method. The convergence properties of the Runge–Kutta finite element method are verified on a numerical example. date: 2015-11 date_type: published official_url: http://dx.doi.org/10.1016/j.aml.2015.05.005 oa_status: green full_text_type: other language: eng primo: open primo_central: open_green article_type_text: Journal Article verified: verified_manual elements_id: 1117102 doi: 10.1016/j.aml.2015.05.005 lyricists_name: Burman, Erik lyricists_id: ENBUR31 actors_name: Burman, Erik actors_id: ENBUR31 actors_role: owner full_text_status: public publication: Applied Mathematics Letters volume: 49 pagerange: 141-146 issn: 1873-5452 citation: Burman, E; (2015) A monotonicity preserving, nonlinear, finite element upwind method for the transport equation. Applied Mathematics Letters , 49 pp. 141-146. 10.1016/j.aml.2015.05.005 <https://doi.org/10.1016/j.aml.2015.05.005>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1476860/1/Burman_upwind_AML.pdf