Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2913 | |
dc.contributor.author | Heida, Martin | |
dc.contributor.author | Sikorski, Alexander | |
dc.contributor.author | Weber, Marcus | |
dc.date.accessioned | 2022-07-08T13:04:38Z | |
dc.date.available | 2022-07-08T13:04:38Z | |
dc.date.issued | 2022 | |
dc.description.abstract | We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $dgeq2$. This results in order of convergence estimates in the natural weighted energy norm and in the weighted discrete $L^2$-norm on admissible meshes. The cells of meshes under consideration may be very irregular in size. We particularly allow the size of certain cells to remain bounded from below even in the asymptotic limit. For uniform meshes we show that the order of convergence is at least 1 in the energy semi-norm, provided the discrete and continuous solutions exist and the continuous solution has $H^2$ regularity. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9671 | |
dc.identifier.uri | https://doi.org/10.34657/8709 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2913 | |
dc.relation.issn | 2198-5855 | |
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 | |
dc.subject.other | Elliptic | eng |
dc.subject.other | finite volume | eng |
dc.subject.other | Voronoi | eng |
dc.title | Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 20 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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