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  <doc>
    <id>8545</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Consistency and order 1 convergence of cell-centered finite volume discretizations of degenerate elliptic problems in any space dimension</title>
    <abstract language="eng">We study consistency of cell-centered finite difference methods for elliptic equations with degenerate coefficients in any space dimension $d \geq 2$. 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.</abstract>
    <parentTitle language="eng">SIAM Journal on Numerical Analysis</parentTitle>
    <identifier type="doi">10.20347/WIAS.PREPRINT.2913</identifier>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Martin Heida</author>
    <submitter>Marcus Weber</submitter>
    <author>Alexander Sikorski</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
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