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  <doc>
    <id>53422</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>12</pageFirst>
    <pageLast>13</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation>Johannes Kepler University</creatingCorporation>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Finite Volume Method in point of view of Finite Element Method</title>
    <abstract language="eng">The best-known discretization methods for solving engineering problems formulated as partial differential equations are finite difference method (FDM), finite element method (FEM) and finite volume method (FVM). While the finite volume method is used in fluid mechanics, the finite element method is predominant in solid state mechanics. At first glance, FVM and FEM are two highly specialized methods. However, both methods can solve problems of both solid mechanics and fluid mechanics well. Since experimental mechanics deals not only with solid state physics but also with fluid mechanics problems, we want to understand FVM in the sense of FEM in this work. In the long term, we want to use the variational calculus to unify many important numerical methods in engineering science into a common framework. In this way, we expect that experiences can be better exchanged between different engineering sciences and thus innovations in the field of experimental mechanics can be advanced. But in this work, we limit ourselves to the understanding of the FVM with the help of the variational calculus already known in FEM. We use a simple 1D Poisson equation to clarify the point. First, we briefly summarize the FVM and FEM. Then we will deal with the actual topic of this paper, as we establish the FEM and the FVM on a common basis by variation formulation. It is shown here that the FVM can be understood in terms of the finite element method with the so-called Galerkin-Petrov approach.</abstract>
    <parentTitle language="eng">Book of Abstracts 37th Danubia Adria Symposium on Advances in Experimental Mechanics</parentTitle>
    <identifier type="isbn">978-3-9504997-0-4</identifier>
    <enrichment key="eventName">37th Danubia Adria Symposium on Advances in Experimental Mechanics</enrichment>
    <enrichment key="eventPlace">Linz, Österreich</enrichment>
    <enrichment key="eventStart">21.09.2021</enrichment>
    <enrichment key="eventEnd">24.09.2021</enrichment>
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    <enrichment key="opus.doi.autoCreate">false</enrichment>
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    <author>Cheng-Chieh Wu</author>
    <author>Daniel Völker</author>
    <author>S. Weisbrich</author>
    <author>F. Neitzel</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite volume method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Variational calculation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Simulation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Computational physics</value>
    </subject>
    <collection role="ddc" number="543">Analytische Chemie</collection>
    <collection role="institutes" number="">8 Zerstörungsfreie Prüfung</collection>
    <collection role="institutes" number="">8.1 Sensorik, mess- und prüftechnische Verfahren</collection>
    <collection role="themenfelder" number="">Umwelt</collection>
    <collection role="fulltextaccess" number="">Datei im Netzwerk der BAM verfügbar ("Closed Access")</collection>
    <collection role="literaturgattung" number="">Graue Literatur</collection>
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  </doc>
  <doc>
    <id>55046</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>2679</pageFirst>
    <pageLast>2683</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>62</volume>
    <type>article</type>
    <publisherName>Elsevier Ltd.</publisherName>
    <publisherPlace>Amsterdam</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The finite volume method in the context of the finite element method</title>
    <abstract language="eng">The finite volume method (FVM), like the finite element method (FEM), is a numerical method for determining an approximate solution for partial differential equations. The derivation of the two methods is based on very different considerations, as they have historically evolved from two distinct engineering disciplines, namely solid mechanics and fluid mechanics. This makes FVM difficult to learn for someone familiar with FEM. In this paper we want to show that a slight modification of the FEM procedure leads to an alternative derivation of the FVM. Both numerical methods are starting from the same strong formulation of the problem represented by differential equations, which are only satisfied by their exact solution. For an approximation of the exact solution, the strong formulation must be converted to a so-called weak form. From here on, the two numerical methods differ. By appropriate choice of the trial function and the test function, we can obtain different numerical methods for solving the weak formulation of the problem. While typically in FEM the basis functions of the trial function and test function are identical, in FVM they are chosen differently. In this paper, we show which trial and test function must be chosen to derive the FVM alternatively: The trial function of the FVM is a “shifted” trial function of the FEM, where the nodal points are now located in the middle of an integration interval rather than at the ends. Moreover, the basis functions of the test function are no longer the same as those of the trial function as in the FEM, but are shown to be a constant equal to 1. This is demonstrated by the example of a 1D Poisson equation.</abstract>
    <parentTitle language="eng">Materials Today: Proceedings</parentTitle>
    <identifier type="issn">2214-7853</identifier>
    <identifier type="doi">10.1016/j.matpr.2022.05.460</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="date_peer_review">18.07.2022</enrichment>
    <author>Cheng-Chieh Wu</author>
    <author>Daniel Völker</author>
    <author>S. Weisbrich</author>
    <author>F. Neitzel</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite Volume Method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite Element Method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Variational Calculation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Numerical Methods</value>
    </subject>
    <collection role="ddc" number="543">Analytische Chemie</collection>
    <collection role="institutes" number="">8 Zerstörungsfreie Prüfung</collection>
    <collection role="institutes" number="">8.1 Sensorik, mess- und prüftechnische Verfahren</collection>
    <collection role="themenfelder" number="">Umwelt</collection>
    <collection role="themenfelder" number="">Chemie und Prozesstechnik</collection>
    <collection role="literaturgattung" number="">Verlagsliteratur</collection>
    <collection role="fulltextaccess" number="">Datei im Netzwerk der BAM verfügbar ("Closed Access")</collection>
    <collection role="themenfelder" number="">Sensorik</collection>
  </doc>
  <doc>
    <id>51551</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>156</pageFirst>
    <pageLast>161</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>32</volume>
    <type>article</type>
    <publisherName>Elsevier Ltd.</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A four-point bending test apparatus for measurement- and model-based structural analysis</title>
    <abstract language="eng">By means of a small-scale truss bridge, the ability of the Measurement- and Model-based Structural Analysis to detect and localise damage was examined in. Although there was no noteworthy difficulty in detecting damage, it turned out that damage localisation responds sensitively to systematic influences, i.e. non-modelled properties of the mechanical model. Therefore, another experiment is being conducted to re-examine the Measurement- and Model-based Structural Analysis. For this purpose, the bending test is carried out as it has been already theoretically respectively numerically discussed in. In this attempt, the systematic influences such as residual stress are kept as low as possible.</abstract>
    <parentTitle language="eng">Materials Today: Proceedings</parentTitle>
    <identifier type="doi">10.1016/j.matpr.2020.04.028</identifier>
    <identifier type="url">http://www.sciencedirect.com/science/article/pii/S2214785320326432</identifier>
    <identifier type="issn">2214-7853</identifier>
    <enrichment key="eventName">36th Danubia Adria Symposium on Advances in Experimental Mechanics</enrichment>
    <enrichment key="eventPlace">Pilsen, Czech Republic</enrichment>
    <enrichment key="eventStart">24.09.2019</enrichment>
    <enrichment key="eventEnd">27.09.2019</enrichment>
    <enrichment key="date_peer_review">03.12.2020</enrichment>
    <author>Cheng-Chieh Wu</author>
    <author>S. Weisbrich</author>
    <author>M. Burger</author>
    <author>F. Neitzel</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Damage detection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Adjustment calculation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Finite element method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integrated analysis</value>
    </subject>
    <collection role="ddc" number="620">Ingenieurwissenschaften und zugeordnete Tätigkeiten</collection>
    <collection role="ddc" number="621">Angewandte Physik</collection>
    <collection role="institutes" number="">8 Zerstörungsfreie Prüfung</collection>
    <collection role="institutes" number="">8.1 Sensorik, mess- und prüftechnische Verfahren</collection>
    <collection role="themenfelder" number="">Infrastruktur</collection>
    <collection role="themenfelder" number="">Material</collection>
    <collection role="themenfelder" number="">Degradationsmechanismen</collection>
    <collection role="literaturgattung" number="">Verlagsliteratur</collection>
    <collection role="fulltextaccess" number="">Datei im Netzwerk der BAM verfügbar ("Closed Access")</collection>
  </doc>
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