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  <doc>
    <id>1079</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-07-10</completedDate>
    <publishedDate>2008-07-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Perturbation Result for Dynamical Contact Problems</title>
    <abstract language="eng">This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.</abstract>
    <identifier type="serial">08-27</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1113</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10793</identifier>
    <enrichment key="SourceTitle">Appeared in: Numer. Math. Theor. Meth. Appl. 2 (2009)</enrichment>
    <author>Corinna Klapproth</author>
    <submitter>unknown unknown</submitter>
    <author>Peter Deuflhard</author>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-27</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Dynamical contact problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>(visco-)elasticity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Signorini condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newmark method</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="35L85">Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]</collection>
    <collection role="msc" number="74H55">Stability</collection>
    <collection role="msc" number="74M15">Contact</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1079/ZR_08_27.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1079/ZR_08_27.ps</file>
  </doc>
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