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<export-example>
  <doc>
    <id>127</id>
    <completedYear>2017</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>97</pageFirst>
    <pageLast>113</pageLast>
    <pageNumber>21</pageNumber>
    <edition/>
    <issue>Vol. 48</issue>
    <volume>Electronic Transactions on Numerical Analysis</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2017-01-02</completedDate>
    <publishedDate>2017-02-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Refinement Strategies for the Simulation of Gas Flow in Networks using a Model Hierarchy</title>
    <abstract language="eng">A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing the simulation error below a prescribed tolerance while keeping the computational costs low. While spatial and temporal stepsize adaptivity is well studied in the literature, model adaptivity is a new field of research. The problem of finding an optimal refinement strategy that combines these three types of adaptivity is a generalisation of the unbounded knapsack problem. A refinement strategy that is currently used in gas flow simulation software is compared to two novel greedy-like strategies. Both a theoretical experiment and a realistic gas flow simulation show that the novel strategies significantly outperform the current refinement strategy with respect to the computational cost incurred.</abstract>
    <identifier type="doi">10.1553/etna_vol48s97</identifier>
    <author>Pia Domschke</author>
    <author>Aseem Dua</author>
    <author>Jeroen J. Stolwijk</author>
    <author>Jens Lang</author>
    <author>Volker Mehrmann</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gas supply networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>model hierarchy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>error estimators</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>model adaptivity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>refinement strategies</value>
    </subject>
    <collection role="institutes" number="">Technische Universität Darmstadt</collection>
    <collection role="institutes" number="">Technische Universität Berlin</collection>
    <collection role="subprojects" number="">B01</collection>
    <collection role="subprojects" number="">B03</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/127/AMC-article.pdf</file>
  </doc>
  <doc>
    <id>224</id>
    <completedYear>2017</completedYear>
    <publishedYear/>
    <thesisYearAccepted>2018</thesisYearAccepted>
    <language>eng</language>
    <pageFirst>779</pageFirst>
    <pageLast>801</pageLast>
    <pageNumber>23</pageNumber>
    <edition/>
    <issue>46(4)</issue>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2017-11-27</completedDate>
    <publishedDate>2017-11-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Model and Discretization Error Adaptivity within Stationary Gas Transport Optimization</title>
    <abstract language="eng">The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and isothermal gas flows. The error control is realized by switching to more detailed models or finer discretizations if necessary to guarantee that a prescribed model and discretization error tolerance is satisfied in the end. We prove convergence of the adaptively controlled optimization method and illustrate the new approach with numerical examples.</abstract>
    <parentTitle language="deu">Vietnam Journal of Mathematics</parentTitle>
    <enrichment key="review.accepted_by">2</enrichment>
    <author>Volker Mehrmann</author>
    <author>Martin Schmidt</author>
    <author>Jeroen J. Stolwijk</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gas network optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Isothermal stationary Euler equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Model hierarchy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Adaptive error control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Marking strategy</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="institutes" number="">Technische Universität Berlin</collection>
    <collection role="subprojects" number="">B03</collection>
    <collection role="subprojects" number="">B08</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/224/nlp-model-coupling_preprint.pdf</file>
  </doc>
</export-example>
