<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>589</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2000-06-20</completedDate>
    <publishedDate>2000-06-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems</title>
    <abstract language="eng">Dynamical process simulation of complex real-life problems often requires the use of modern algorithms, which automatically adapt both the time and space discretization in order to get error-controlled approximations of the solution. In this paper, a combination of linearly implicit time integrators of Rosenbrock type and adaptive multilevel finite elements based on a posteriori error estimates is presented. This approach has proven to work quite satisfactorily for a wide range of challenging practical problems. We show the performance of our adaptive method for two applications that arise in the study of flame balls and brine transport in porous media.</abstract>
    <identifier type="serial">00-21</identifier>
    <identifier type="opus3-id">590</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-5892</identifier>
    <enrichment key="SourceTitle">Appeared in: A. V. Wouver; P. Saucez; W. E. Schiesser (eds.), Adaptive Method of Lines, Chapman and Hall, CRC, 2001, ISBN: 1-58488-231-X, pp. 295-316</enrichment>
    <author>Jens Lang</author>
    <author>Bodo Erdmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>00-21</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear time-dependent PDEs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Rosenbrock methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multilevel finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>local refinement</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>a posteriori error estimates</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/589/ZR-00-21.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/589/ZR-00-21.pdf</file>
  </doc>
</export-example>
