<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>26735</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>A1226</pageFirst>
    <pageLast>A1244</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>42</volume>
    <type>articler</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-01-14</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Numerical Approximation of Optimal Convex Shapes</title>
    <abstract language="eng">This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem. Moreover, we prove the convergence of discretizations in two-dimensional situations. A numerical algorithm is devised that iteratively solves the discrete formulation. Numerical experiments show that optimal convex shapes are generally nonsmooth and that three-dimensional problems require an appropriate relaxation of the convexity condition.</abstract>
    <parentTitle language="eng">SIAM Journal on Scientific Computing</parentTitle>
    <identifier type="issn">1095-7197</identifier>
    <identifier type="issn">1064-8275</identifier>
    <identifier type="doi">10.1137/19M1256853</identifier>
    <enrichment key="BTU">an der BTU erstellt / created at BTU</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="Fprofil">1 Energiewende und Dekarbonisierung / Energy Transition and Decarbonisation</enrichment>
    <enrichment key="Fprofil">4 Künstliche Intelligenz und Sensorik / Artificial Intelligence and Sensor Technology</enrichment>
    <author>
      <firstName>Sören</firstName>
      <lastName>Bartels</lastName>
    </author>
    <submitter>
      <firstName>Helen</firstName>
      <lastName>Jacob</lastName>
    </submitter>
    <author>
      <firstName>Gerd</firstName>
      <lastName>Wachsmuth</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shape optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>PDE constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convexity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convergence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>iterative solution</value>
    </subject>
    <collection role="institutes" number="1309">FG Optimale Steuerung</collection>
  </doc>
</export-example>
