Show simple item record

dc.contributor.authorChristiansen, Thomas
dc.contributor.authorGrunert, Katrin
dc.contributor.authorNordli, Anders Samuelsen
dc.contributor.authorSolem, Susanne
dc.date.accessioned2024-03-08T14:50:31Z
dc.date.available2024-03-08T14:50:31Z
dc.date.issued2024-03-02
dc.description.abstractA convergent numerical method for α -dissipative solutions of the Hunter–Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized method of characteristics. The projection step is the only step that introduces any approximation error. It is therefore crucial that its design ensures not only a good approximation of the initial data, but also that errors due to the energy dissipation at later times remain small. Furthermore, it is shown that the main quantity of interest, the wave profile, converges in L<sup>∞</sup> for all t≥0 , while a subsequence of the energy density converges weakly for almost every time.en_US
dc.identifier.citationChristiansen T, Grunert K, Nordli AS, Solem S. A Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equation. Journal of Scientific Computing. 2024;99(14)en_US
dc.identifier.cristinIDFRIDAID 2252012
dc.identifier.doi10.1007/s10915-024-02479-4
dc.identifier.issn0885-7474
dc.identifier.issn1573-7691
dc.identifier.urihttps://hdl.handle.net/10037/33146
dc.language.isoengen_US
dc.publisherSpringer Natureen_US
dc.relation.journalJournal of Scientific Computing
dc.relation.projectIDNorges forskningsråd: 250070en_US
dc.relation.projectIDNorges forskningsråd: 286822en_US
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2024 The Author(s)en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0en_US
dc.rightsAttribution 4.0 International (CC BY 4.0)en_US
dc.subjectVDP::Matematikk og naturvitenskap: 400en_US
dc.subjectVDP::Mathematics and natural scienses: 400en_US
dc.subjectIkke-lineære hyperbolske PDEer / Non-linear hyperbolic PDEsen_US
dc.subjectNumerikk / Numericsen_US
dc.titleA Convergent Numerical Algorithm for α-Dissipative Solutions of the Hunter–Saxton Equationen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


File(s) in this item

Thumbnail

This item appears in the following collection(s)

Show simple item record

Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's license is described as Attribution 4.0 International (CC BY 4.0)