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Analysis of the stabilized element free Galerkin approximations to the Stokes equations.

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Title: Analysis of the stabilized element free Galerkin approximations to the Stokes equations.
Authors: Kamranian, Maryam1 (AUTHOR) m.kamranian@aut.ac.ir, Tatari, Mehdi1,2,3 (AUTHOR) mtatari@cc.iut.ac.ir, Dehghan, Mehdi1 (AUTHOR) mdehghan.aut@gmail.com
Source: Applied Numerical Mathematics. Apr2020, Vol. 150, p325-340. 16p.
Subjects: Stokes equations, Galerkin methods, Least squares, Sobolev spaces
Abstract: This paper introduces an element free Galerkin method for solving Stokes equations based on the velocity-pressure formulation. A consistently stabilized element free Galerkin method is proposed and Nitsche's method is applied. We formulate and study the optimal convergence of this method. For this purpose, the concept of the vector-valued moving least squares approximation is employed to derive the error estimation in Sobolev spaces. Finally we report some numerical experiments to illustrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 140920264
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Analysis of the stabilized element free Galerkin approximations to the Stokes equations.
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  Data: <searchLink fieldCode="AR" term="%22Kamranian%2C+Maryam%22">Kamranian, Maryam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> m.kamranian@aut.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Tatari%2C+Mehdi%22">Tatari, Mehdi</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> mtatari@cc.iut.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Dehghan%2C+Mehdi%22">Dehghan, Mehdi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mdehghan.aut@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Apr2020, Vol. 150, p325-340. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Stokes+equations%22">Stokes equations</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink><br /><searchLink fieldCode="DE" term="%22Sobolev+spaces%22">Sobolev spaces</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper introduces an element free Galerkin method for solving Stokes equations based on the velocity-pressure formulation. A consistently stabilized element free Galerkin method is proposed and Nitsche's method is applied. We formulate and study the optimal convergence of this method. For this purpose, the concept of the vector-valued moving least squares approximation is employed to derive the error estimation in Sobolev spaces. Finally we report some numerical experiments to illustrate the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.apnum.2019.10.002
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 325
    Subjects:
      – SubjectFull: Stokes equations
        Type: general
      – SubjectFull: Galerkin methods
        Type: general
      – SubjectFull: Least squares
        Type: general
      – SubjectFull: Sobolev spaces
        Type: general
    Titles:
      – TitleFull: Analysis of the stabilized element free Galerkin approximations to the Stokes equations.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Kamranian, Maryam
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          Name:
            NameFull: Tatari, Mehdi
      – PersonEntity:
          Name:
            NameFull: Dehghan, Mehdi
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          Dates:
            – D: 01
              M: 04
              Text: Apr2020
              Type: published
              Y: 2020
          Identifiers:
            – Type: issn-print
              Value: 01689274
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            – Type: volume
              Value: 150
          Titles:
            – TitleFull: Applied Numerical Mathematics
              Type: main
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