Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1443 | |
dc.contributor.author | Glitzky, Annegret | |
dc.date.accessioned | 2016-03-24T17:38:32Z | |
dc.date.available | 2019-06-28T08:04:23Z | |
dc.date.issued | 2009 | |
dc.description.abstract | Our focus are energy estimates for discretized reaction-diffusion systems for a finite number of species. We introduce a discretization scheme (Voronoi finite volume in space and fully implicit in time) which has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation. For a class of Voronoi finite volume meshes we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the discrete free energy to its equilibrium value with a unified rate of decay for this class of discretizations. The fundamental idea is an estimate of the free energy by the dissipation rate which is proved indirectly by taking into account sequences of Voronoi finite volume meshes. Essential ingredient in that proof is a discrete Sobolev- Poincaré inequality. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/3453 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2182 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This 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.license | Dieses 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.ddc | 510 | eng |
dc.subject.other | Reaction-diffusion systems | eng |
dc.subject.other | energy estimates | eng |
dc.subject.other | thermodynamic equilibria | eng |
dc.subject.other | asymptotic behaviour | eng |
dc.subject.other | time and space discretization | eng |
dc.subject.other | boundary conforming Delaunay grid | eng |
dc.subject.other | Voronoi finite volume scheme | eng |
dc.subject.other | discrete Sobolev-Poincar´e inequality | eng |
dc.title | Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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