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A Partition of Unity Method for a Fourth‐Order Variational Inequality of the Second Kind.

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Title: A Partition of Unity Method for a Fourth‐Order Variational Inequality of the Second Kind.
Authors: Bard Davis, Christopher1 (AUTHOR) cbdavis@tntech.edu, Zhang, Yi2 (AUTHOR)
Source: Numerical Methods for Partial Differential Equations. Jul2025, Vol. 41 Issue 4, p1-13. 13p.
Subjects: Partition of unity method, Variational inequalities (Mathematics), Energy function, Error analysis in mathematics
Abstract: In this work, we consider the use of a flat‐top partition of unity method to solve a class of fourth‐order variational inequalities of the second kind. Under the assumption that the solution is H3(Ω)$$ {H}^3\left(\Omega \right) $$ regular, optimal error estimates are made in the energy norm. Numerical examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
Copyright of Numerical Methods for Partial Differential Equations is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: A Partition of Unity Method for a Fourth‐Order Variational Inequality of the Second Kind.
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  Data: <searchLink fieldCode="AR" term="%22Bard+Davis%2C+Christopher%22">Bard Davis, Christopher</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cbdavis@tntech.edu</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Yi%22">Zhang, Yi</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Numerical+Methods+for+Partial+Differential+Equations%22">Numerical Methods for Partial Differential Equations</searchLink>. Jul2025, Vol. 41 Issue 4, p1-13. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+inequalities+%28Mathematics%29%22">Variational inequalities (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+function%22">Energy function</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: In this work, we consider the use of a flat‐top partition of unity method to solve a class of fourth‐order variational inequalities of the second kind. Under the assumption that the solution is H3(Ω)$$ {H}^3\left(\Omega \right) $$ regular, optimal error estimates are made in the energy norm. Numerical examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Numerical Methods for Partial Differential Equations is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1002/num.70020
    Languages:
      – Code: eng
        Text: English
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        PageCount: 13
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    Subjects:
      – SubjectFull: Partition of unity method
        Type: general
      – SubjectFull: Variational inequalities (Mathematics)
        Type: general
      – SubjectFull: Energy function
        Type: general
      – SubjectFull: Error analysis in mathematics
        Type: general
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      – TitleFull: A Partition of Unity Method for a Fourth‐Order Variational Inequality of the Second Kind.
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            NameFull: Bard Davis, Christopher
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            NameFull: Zhang, Yi
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            – D: 01
              M: 07
              Text: Jul2025
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              Y: 2025
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              Value: 41
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            – TitleFull: Numerical Methods for Partial Differential Equations
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