Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes

Hdl Handle:
http://hdl.handle.net/10034/609023
Title:
Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes
Authors:
Barrenechea, Gabriel; Burman, Erik; Karakatsani, Fotini
Abstract:
For the case of approximation of convection–diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.
Affiliation:
University of Strathclyde; University College London; University of Chester
Citation:
Barrenechea, G., Burman, E. & Karakatsani, F. (2016). Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes. Numerische Mathematik, 135(2), 521-545. http://dx.doi.org/10.1007/s00211-016-0808-z
Publisher:
Springer
Journal:
Numerische Mathematik
Publication Date:
7-May-2016
URI:
http://hdl.handle.net/10034/609023
DOI:
10.1007/s00211-016-0808-z
Additional Links:
http://link.springer.com/article/10.1007/s00211-016-0808-z
Type:
Article
Language:
en
Description:
The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-016-0808-z
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorBarrenechea, Gabrielen
dc.contributor.authorBurman, Eriken
dc.contributor.authorKarakatsani, Fotinien
dc.date.accessioned2016-05-11T09:02:09Zen
dc.date.available2016-05-11T09:02:09Zen
dc.date.issued2016-05-07en
dc.identifier.citationBarrenechea, G., Burman, E. & Karakatsani, F. (2016). Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes. Numerische Mathematik, 135(2), 521-545. http://dx.doi.org/10.1007/s00211-016-0808-zen
dc.identifier.doi10.1007/s00211-016-0808-zen
dc.identifier.urihttp://hdl.handle.net/10034/609023en
dc.descriptionThe final publication is available at Springer via http://dx.doi.org/10.1007/s00211-016-0808-z-
dc.description.abstractFor the case of approximation of convection–diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.en
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urlhttp://link.springer.com/article/10.1007/s00211-016-0808-zen
dc.rightsAn error occurred on the license name.*
dc.rights.uriAn error occurred getting the license - uri.en
dc.subject65N30en
dc.subject65N12en
dc.titleEdge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemesen
dc.typeArticleen
dc.contributor.departmentUniversity of Strathclyde; University College London; University of Chesteren
dc.identifier.journalNumerische Mathematiken
dc.date.accepted2016-04-11en
or.grant.openaccessYesen
rioxxterms.funderLeverhulme Trusten
rioxxterms.identifier.projectRPG-2012-483en
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2017-05-07en
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