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  <doc>
    <id>1049</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-12-21</completedDate>
    <publishedDate>2007-12-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations</title>
    <abstract language="eng">Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples.</abstract>
    <identifier type="serial">07-45</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1078</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10493</identifier>
    <enrichment key="SourceTitle">Appeared in: Applied Numerical Mathematics 59 (2009), pp. 1858-1869. DOI information: 10.1016/j.apnum.2009.01.010</enrichment>
    <author>Martin Weiser</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>07-45</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction-diffusion equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>travelling waves</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonlinear scaling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discretization error</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="65M50">Mesh generation and refinement</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ZIB-Cardio">ZIB-Cardio</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1049/ZR_07_45.pdf</file>
  </doc>
</export-example>
