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  <doc>
    <id>418</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-09-01</completedDate>
    <publishedDate>2021-09-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An asymptotic-preserving discretization scheme for gas transport in pipe networks</title>
    <abstract language="eng">We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and an implicit Euler method in time. Assuming the existence of a smooth subsonic solution bounded away from vacuum, a full convergence analysis is presented based on relative energy estimates. &#13;
&#13;
Particular attention is paid to establishing error bounds that are uniform in the friction parameter. As a consequence, the method and results also cover the parabolic problem arising in the asymptotic large friction limit. &#13;
&#13;
The error estimates are derived in detail for a single pipe, but using appropriate coupling conditions and the particular structure of the problem and its discretization, the main results directly generalize to pipe networks. &#13;
&#13;
Numerical tests are presented for illustration.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY-NC - Namensnennung - Nicht kommerziell 4.0 International</licence>
    <author>Herbert Egger</author>
    <author>Jan Giesselmann</author>
    <author>Nora Philippi</author>
    <author>Teresa Kunkel</author>
    <collection role="institutes" number="">Technische Universität Darmstadt</collection>
    <collection role="subprojects" number="">C04</collection>
    <collection role="subprojects" number="">C05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/418/relativeenergy.pdf</file>
  </doc>
  <doc>
    <id>562</id>
    <completedYear>2024</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-10-11</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Identification of minimal number of measurements allowing synchronization of a nodal observer for the wave equation</title>
    <abstract language="eng">We study a state estimation problem for a 2x2 linear hyperbolic system on networks with eigenvalues with opposite signs. The system can be seen as a simplified model for gas flow through gas networks. For this system we construct an observer system based on nodal measurements and investigate the convergence of the state of the observer system towards the original system state. We assume that measurements are available at the boundary nodes of the network and identify the minimal number of additional measurements in the network that are needed to guarantee synchronization of the observer state towards the original system state. It turns out that for tree-shaped networks boundary measurements suffice to guarantee exponential synchronization, while for networks that contain cycles synchronization can be guaranteed if and only if at least one measurement point is added in each cycle. This is shown for a system without source term and for a system with linear friction term.</abstract>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International</licence>
    <author>Jan Giesselmann</author>
    <author>Teresa Kunkel</author>
    <collection role="institutes" number="">Technische Universität Darmstadt</collection>
    <collection role="subprojects" number="">C05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/562/BoundaryObserver.pdf</file>
  </doc>
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