Mixed covolume methods for quasi-linear second-order elliptic problems

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dc.contributor.authorKwak, Do Youngko
dc.contributor.authorKim, KYko
dc.date.accessioned2013-03-02T21:10:43Z-
dc.date.available2013-03-02T21:10:43Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2000-11-
dc.identifier.citationSIAM JOURNAL ON NUMERICAL ANALYSIS, v.38, no.4, pp.1057 - 1072-
dc.identifier.issn0036-1429-
dc.identifier.urihttp://hdl.handle.net/10203/75529-
dc.description.abstractWe consider covolume methods for the mixed formulations of quasi-linear second-order elliptic problems. Covolume methods for the mixed formulations of linear elliptic problem was rst considered by Russell [Rigorous Block-Centered Discretizations on Irregular Grids: Improved Simulation of Complex Reservoir Systems, Tech. report 3, Project Report, Reservoir Simulation Research Corporation, Tulsa, OK, 1995] and tested extensively in [ Cai et al., Comput. Geosci., 1( 1997), pp. 289-315], [Jones, A Mixed Finite Volume Element Method for Accurate Computation of Fluid Velocities in Porous Media, Ph. D. thesis, University of Colorado, Denver, 1995]. The analysis was carried out by Chou and Kwak [SIAM J. Numer. Anal., 37 (2000), pp. 758-771] for linear symmetric problems, where they showed optimal error estimates in L-2 norm for the pressure and in H ( div) norm for the velocity. In this paper we extend their results to quasi-linear problems by following Milner's argument [Math. Comp., 44 (1985), pp. 303-320] through an adaptation of the duality argument of Douglas and Roberts [Math. Comp., 44 (1985), pp. 39-52] for mixed covolume methods.-
dc.languageEnglish-
dc.publisherSIAM PUBLICATIONS-
dc.subjectCENTERED FINITE-DIFFERENCES-
dc.subjectVOLUME ELEMENT METHOD-
dc.subjectCONSERVATION-LAWS-
dc.subjectCONVERGENCE-
dc.subjectGRIDS-
dc.subjectEQUATIONS-
dc.subjectSCHEMES-
dc.titleMixed covolume methods for quasi-linear second-order elliptic problems-
dc.typeArticle-
dc.identifier.wosid000165318700001-
dc.identifier.scopusid2-s2.0-0346524797-
dc.type.rimsART-
dc.citation.volume38-
dc.citation.issue4-
dc.citation.beginningpage1057-
dc.citation.endingpage1072-
dc.citation.publicationnameSIAM JOURNAL ON NUMERICAL ANALYSIS-
dc.contributor.localauthorKwak, Do Young-
dc.contributor.nonIdAuthorKim, KY-
dc.type.journalArticleArticle-
dc.subject.keywordAuthormixed method-
dc.subject.keywordAuthorcovolume method-
dc.subject.keywordAuthorquasi-linear elliptic problems-
dc.subject.keywordPlusCENTERED FINITE-DIFFERENCES-
dc.subject.keywordPlusVOLUME ELEMENT METHOD-
dc.subject.keywordPlusCONSERVATION-LAWS-
dc.subject.keywordPlusCONVERGENCE-
dc.subject.keywordPlusGRIDS-
dc.subject.keywordPlusEQUATIONS-
dc.subject.keywordPlusSCHEMES-
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