1 Ocak 2018 Dergi makalesi Açık Erişim

Aksoylu, Burak; Kaya, Adem

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/31361</identifier>
  <creators>
    <creator>
      <creatorName>Aksoylu, Burak</creatorName>
      <givenName>Burak</givenName>
      <familyName>Aksoylu</familyName>
    </creator>
    <creator>
      <creatorName>Kaya, Adem</creatorName>
      <givenName>Adem</givenName>
      <familyName>Kaya</familyName>
      <affiliation>Izmir Inst Technol, Dept Math, TR-35430 Izmir, Turkey</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Conditioning And Error Analysis Of Nonlocal Operators With Local Boundary Conditions</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2018</publicationYear>
  <dates>
    <date dateType="Issued">2018-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/31361</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1016/j.cam.2017.11.023</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">We study the conditioning and error analysis of novel nonlocal operators in ID with local boundary conditions. These operators are used, for instance, in peridynamics (PD) and nonlocal diffusion. The original PD operator uses nonlocal boundary conditions (BC). The novel operators agree with the original PD operator in the bulk of the domain and simultaneously enforce local periodic, antiperiodic, Neumann, or Dirichlet BC. We prove sharp bounds for their condition numbers in the parameter delta only, the size of nonlocality. We accomplish sharpness both rigorously and numerically. We also present an error analysis in which we use the Nystrom method with the trapezoidal rule for discretization. Using the sharp bounds, we prove that the error bound scales like O(h(2)delta(-2)) and verify the bound numerically.</description>
  </descriptions>
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