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  <doc>
    <id>88</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-09-01</completedDate>
    <publishedDate>1992-09-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux.</title>
    <abstract language="eng">A new adaptive approach for one-dimensional scalar conservation laws with convex flux is proposed. The initial data are approximated on an adaptive grid by a problem dependent, monotone interpolation procedure in such a way, that the multivalued problem of characteristic transport can be easily and explicitly solved. The unique entropy solution is chosen by means of a selection criterion due to LAX. For arbitrary times, the solutions is represented by an adaptive monotone spline interpolation. The spatial approximation is controlled by local $L^1$-error estimated. As a distinctive feature of the approach, there is no discretization in time. The method is monotone on fixed grids. Numerical examples are included, to demonstrate the predicted behavior. {\bf Key words.} method of characteristics, adaptive grids, monotone interpolation, $L^1$-error estimates {\bf AMS(MOS) subject classification.} 65M15, 65M25, 65M50.</abstract>
    <identifier type="serial">SC-92-18</identifier>
    <identifier type="opus3-id">87</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-880</identifier>
    <enrichment key="SourceTitle">Appeared in: Proc. of the Ninth GAMM-Seminar Kiel, 1993 on Adaptive Methods: Algorithms, Theory and Applications. W. Hackbusch, G. Wittum (eds.) Braunschweig: Vieweg 1994, pp. 69-83</enrichment>
    <author>Folkmar A. Bornemann</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>method of characteristics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive grids</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>monotone interpolation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>L1-error estimates</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65M15">Error bounds</collection>
    <collection role="msc" number="65M25">Method of characteristics</collection>
    <collection role="msc" number="65M50">Mesh generation and refinement</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/88/SC-92-18.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/88/SC-92-18.pdf</file>
  </doc>
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