Blending low-order stabilised finite element methods: a positivity preserving local projection method for the convection-diffusion equation

Hdl Handle:
http://hdl.handle.net/10034/620327
Title:
Blending low-order stabilised finite element methods: a positivity preserving local projection method for the convection-diffusion equation
Authors:
Barrenechea, Gabriel; Burman, Erik; Karakatsani, Fotini
Abstract:
In this work we propose a nonlinear blending of two low-order stabilisation mechanisms for the convection–diffusion equation. The motivation for this approach is to preserve monotonicity without sacrificing accuracy for smooth solutions. The approach is to blend a first-order artificial diffusion method, which will be active only in the vicinity of layers and extrema, with an optimal order local projection stabilisation method that will be active on the smooth regions of the solution. We prove existence of discrete solutions, as well as convergence, under appropriate assumptions on the nonlinear terms, and on the exact solution. Numerical examples show that the discrete solution produced by this method remains within the bounds given by the continuous maximum principle, while the layers are not smeared significantly.
Affiliation:
University of Strathclyde; UCL; University of Chester
Citation:
Barrenechea, G. R., et. al. (2017). Blending low-order stabilised finite element methods: a positivity preserving local projection method for the convection-diffusion equation. Computer Methods in Applied Mechanics and Engineering, 317, 1169-1193. DOI: 10.1016/j.cma.2017.01.2016
Publisher:
Elsevier
Journal:
Computer Methods in Applied Mechanics and Engineering
Publication Date:
20-Jan-2017
URI:
http://hdl.handle.net/10034/620327
DOI:
10.1016/j.cma.2017.01.016
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0045782517300841
Type:
Article
Language:
en
EISSN:
1879-2138
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorBarrenechea, Gabrielen
dc.contributor.authorBurman, Eriken
dc.contributor.authorKarakatsani, Fotinien
dc.date.accessioned2017-01-26T14:03:05Z-
dc.date.available2017-01-26T14:03:05Z-
dc.date.issued2017-01-20-
dc.identifier.citationBarrenechea, G. R., et. al. (2017). Blending low-order stabilised finite element methods: a positivity preserving local projection method for the convection-diffusion equation. Computer Methods in Applied Mechanics and Engineering, 317, 1169-1193. DOI: 10.1016/j.cma.2017.01.2016en
dc.identifier.doi10.1016/j.cma.2017.01.016-
dc.identifier.urihttp://hdl.handle.net/10034/620327-
dc.description.abstractIn this work we propose a nonlinear blending of two low-order stabilisation mechanisms for the convection–diffusion equation. The motivation for this approach is to preserve monotonicity without sacrificing accuracy for smooth solutions. The approach is to blend a first-order artificial diffusion method, which will be active only in the vicinity of layers and extrema, with an optimal order local projection stabilisation method that will be active on the smooth regions of the solution. We prove existence of discrete solutions, as well as convergence, under appropriate assumptions on the nonlinear terms, and on the exact solution. Numerical examples show that the discrete solution produced by this method remains within the bounds given by the continuous maximum principle, while the layers are not smeared significantly.en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0045782517300841en
dc.subject65N12en
dc.subject65N30en
dc.titleBlending low-order stabilised finite element methods: a positivity preserving local projection method for the convection-diffusion equationen
dc.typeArticleen
dc.identifier.eissn1879-2138-
dc.contributor.departmentUniversity of Strathclyde; UCL; University of Chesteren
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.date.accepted2017-01-10-
or.grant.openaccessYesen
rioxxterms.funderPartially funded by the Leverhulme Trusten
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2019-01-20-
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