Stability of explicit one-step methods for P1-finite element approximation of linear diffusion equations on anisotropic meshes

dc.contributor.authorHuang, Weizhang
dc.contributor.authorKamenski, Lennard
dc.contributor.authorLang, Jens
dc.date.accessioned2017-01-04T16:09:58Z
dc.date.available2019-06-28T08:03:41Z
dc.date.issued2016
dc.description.abstractWe study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix within a factor of 2(d+1), where d is the spatial dimension. Both full mass matrix and mass lumping are considered. The bound reveals that the stability condition is affected by two factors. The first one depends on the number of mesh elements and corresponds to the classic bound for the Laplace operator on a uniform mesh. The other factor reflects the effects of the interplay of the mesh geometry and the diffusion matrix. It is shown that it is not the mesh geometry itself but the mesh geometry in relation to the diffusion matrix that is crucial to the stability of explicit methods. When the mesh is uniform in the metric specified by the inverse of the diffusion matrix, the stability condition is comparable to the situation with the Laplace operator on a uniform mesh. Numerical results are presented to verify the theoretical findings.eng
dc.description.versionpublishedVersioneng
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/2080
dc.language.isoengeng
dc.publisherPhiladelphia : Society for Industrial and Applied Mathematicseng
dc.relation.doihttps://doi.org/10.1137/130949531
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.subject.ddc510eng
dc.subject.otherFinite element methodeng
dc.subject.otheranisotropic mesheng
dc.subject.otherstability conditioneng
dc.subject.otherparabolic equationeng
dc.subject.otherexplicit one-step methodeng
dc.titleStability of explicit one-step methods for P1-finite element approximation of linear diffusion equations on anisotropic mesheseng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
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