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    <id>84</id>
    <completedYear/>
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    <thesisYearAccepted/>
    <language>eng</language>
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    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-06-04</completedDate>
    <publishedDate>1992-06-04</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Multilevel-Methods in 3-Space Dimensions.</title>
    <abstract language="eng">We consider the approximate solution of selfadjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. as the performance of hierarchical bases preconditioners deteriorate in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a-posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real-life problem arising from hyperthermia, a recent clinical method for cancer therapy.</abstract>
    <identifier type="serial">SC-92-14</identifier>
    <identifier type="opus3-id">83</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-843</identifier>
    <enrichment key="SourceTitle">Appeared in: International Journal for Numerical Methods in Engineering, Vol. 36, pp. 3187-3203 (1993)</enrichment>
    <author>Folkmar A. Bornemann</author>
    <author>Bodo Erdmann</author>
    <author>Ralf Kornhuber</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-14</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/84/SC-92-14.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/84/SC-92-14.pdf</file>
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  <doc>
    <id>76</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-04-01</completedDate>
    <publishedDate>1992-04-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Discretization and Iterative Solution of Convection Diffusion Equations.</title>
    <abstract language="eng">We propose an extended box method which turns out to be a variant of standard finite element methods in the case of pure diffusion and an extension of backward differencing to irregular grids if only convective transport is present. Together with the adaptive orientation proposed in a recent paper and a streamline ordering of the unknowns, this discretization leads to a highly efficient adaptive method for the approximation of internal layers in the case of large local Peclet numbers.</abstract>
    <identifier type="serial">SC-92-06</identifier>
    <identifier type="opus3-id">75</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-762</identifier>
    <enrichment key="SourceTitle">Appeared in: W. Hackbusch, G. Wittum (eds.) Incomplete Decompositions (ILU) - Algorithms, Theory and Applications. Vieweg, Braunschweig, 1993, Notes on Numerical Fluid Mechanics, Vol. 41, pp. 67-77</enrichment>
    <author>Ralf Kornhuber</author>
    <author>Gabriel Wittum</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-06</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/76/SC-92-06.pdf</file>
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