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