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  <doc>
    <id>1190</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-12-14</completedDate>
    <publishedDate>2010-12-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox</title>
    <abstract language="eng">This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.</abstract>
    <identifier type="serial">10-25</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1253</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11909</identifier>
    <enrichment key="SourceTitle">Appeared in:  A. Dedner  et al. (eds.) Advances in DUNE. Springer, 2012. 101-112</enrichment>
    <author>Sebastian Götschel</author>
    <submitter>unknown unknown</submitter>
    <author>Martin Weiser</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-25</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>partial differential equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>finite elements</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>generic programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptive methods</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65Y99">None of the above, but in this section</collection>
    <collection role="msc" number="68U20">Simulation [See also 65Cxx]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-F9">MATHEON-F9</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1190/ZR_10_25.pdf</file>
  </doc>
  <doc>
    <id>1193</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-12-22</completedDate>
    <publishedDate>2010-12-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Uniqueness criteria for solutions of the adjoint equation in state-constrained optimal control</title>
    <abstract language="eng">The paper considers linear elliptic equations with regular Borel measures as inhomogeneity. Such equations frequently appear in state-constrained optimal control&#13;
problems. By a counter-example of Serrin, it is known that, in the presence of&#13;
non-smooth data, a standard weak formulation does not ensure uniqueness for such&#13;
equations. Therefore several notions of solution have been developed that guarantee&#13;
uniqueness. In this note, we compare different definitions of solutions, namely the ones&#13;
of Stampacchia and the two notions of solutions of Casas and Alibert-Raymond, and show that they are the same. As side results, we reformulate the solution&#13;
in the sense of Stampacchia, and prove the existence and uniqueness of solutions in&#13;
in case of mixed boundary conditions.</abstract>
    <identifier type="serial">10-28</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11933</identifier>
    <author>Christian Meyer</author>
    <submitter>-empty- (Opus4 user: admin)</submitter>
    <author>Lucia Panizzi</author>
    <submitter>Anton Schiela</submitter>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-28</number>
    </series>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>elliptic partial differential equations</value>
    </subject>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language/>
      <type>uncontrolled</type>
      <value>measure right hand sides</value>
    </subject>
    <collection role="msc" number="35D99">None of the above, but in this section</collection>
    <collection role="msc" number="46N10">Applications in optimization, convex analysis, mathematical programming, economics</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1193/ZR-10-28.pdf</file>
  </doc>
  <doc>
    <id>1171</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-06-09</completedDate>
    <publishedDate>2010-06-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive Timestep Control for the Contact-Stabilized Newmark Method</title>
    <abstract language="eng">The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.</abstract>
    <identifier type="serial">10-09</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1232</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11714</identifier>
    <enrichment key="SourceTitle">Appeared in: Numerische Mathematik vol. 119 iss. 1 (2011), pp. 49-81</enrichment>
    <author>Corinna Klapproth</author>
    <submitter>unknown unknown</submitter>
    <author>Anton Schiela</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>dynamical contact problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>contact--stabilized Newmark method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>extrapolation methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>adaptivity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>timestep control</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="35L86">Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1171/adaptivity.pdf</file>
  </doc>
  <doc>
    <id>4678</id>
    <completedYear/>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>419</pageFirst>
    <pageLast>428</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>incollection</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Barrier methods for a control problem from hyperthermia treatment planning</title>
    <abstract language="eng">We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.</abstract>
    <parentTitle language="eng">Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009)</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-11567</enrichment>
    <author>Anton Schiela</author>
    <editor>M. Diehl</editor>
    <submitter>Martin Weiser</submitter>
    <author>Martin Weiser</author>
    <editor>F. Glineur</editor>
    <editor>E. Jarlebring</editor>
    <editor>W. Michiels</editor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
  </doc>
</export-example>
