View in EDS

A Priori and a Posteriori Error Analyses of a Pressure-Robust Virtual Element Method for the Two-Dimensional Brinkman problem.

Saved in:
Bibliographic Details
Title: A Priori and a Posteriori Error Analyses of a Pressure-Robust Virtual Element Method for the Two-Dimensional Brinkman problem.
Authors: Xiong, Yu1 (AUTHOR) xtuyuriyxiong@gmail.com, Chen, Yanping2 (AUTHOR) ypchen@njupt.edu.cn, Zhou, Jianwei3 (AUTHOR) jwzhou@yahoo.com, Zhou, Yanping4 (AUTHOR) zhyp5208@163.com, Huang, Jian1 (AUTHOR) huangjian213@xtu.edu.cn
Source: Journal of Scientific Computing. Feb2026, Vol. 106 Issue 2, p1-35. 35p.
Abstract: This article investigates both a priori and a posteriori error estimates for a pressure-robust and divergence-free virtual element method to approximate the incompressible Brinkman problem on polygonal meshes. The exactly divergence-free property of virtual space preserves the mass-conservation of the system. By extending the lowest-order Raviart–Thomas element to polygonal meshes, we construct a divergence-preserving reconstructor for the discretization of the right-hand side. A rigorous a priori error analysis is developed, showing that the velocity error is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method’s ability to handle more general polygonal meshes, we design an adaptive mesh refinement approach and construct a residual-type a posteriori error indicator. This indicator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Scientific Computing is the property of Springer Nature 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
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 190972729
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: A Priori and a Posteriori Error Analyses of a Pressure-Robust Virtual Element Method for the Two-Dimensional Brinkman problem.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Xiong%2C+Yu%22">Xiong, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xtuyuriyxiong@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Chen%2C+Yanping%22">Chen, Yanping</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> ypchen@njupt.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhou%2C+Jianwei%22">Zhou, Jianwei</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> jwzhou@yahoo.com</i><br /><searchLink fieldCode="AR" term="%22Zhou%2C+Yanping%22">Zhou, Yanping</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> zhyp5208@163.com</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Jian%22">Huang, Jian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> huangjian213@xtu.edu.cn</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Scientific+Computing%22">Journal of Scientific Computing</searchLink>. Feb2026, Vol. 106 Issue 2, p1-35. 35p.
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This article investigates both a priori and a posteriori error estimates for a pressure-robust and divergence-free virtual element method to approximate the incompressible Brinkman problem on polygonal meshes. The exactly divergence-free property of virtual space preserves the mass-conservation of the system. By extending the lowest-order Raviart–Thomas element to polygonal meshes, we construct a divergence-preserving reconstructor for the discretization of the right-hand side. A rigorous a priori error analysis is developed, showing that the velocity error is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method’s ability to handle more general polygonal meshes, we design an adaptive mesh refinement approach and construct a residual-type a posteriori error indicator. This indicator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Scientific Computing is the property of Springer Nature 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.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190972729
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10915-026-03186-y
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 35
        StartPage: 1
    Titles:
      – TitleFull: A Priori and a Posteriori Error Analyses of a Pressure-Robust Virtual Element Method for the Two-Dimensional Brinkman problem.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Xiong, Yu
      – PersonEntity:
          Name:
            NameFull: Chen, Yanping
      – PersonEntity:
          Name:
            NameFull: Zhou, Jianwei
      – PersonEntity:
          Name:
            NameFull: Zhou, Yanping
      – PersonEntity:
          Name:
            NameFull: Huang, Jian
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 08857474
          Numbering:
            – Type: volume
              Value: 106
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Journal of Scientific Computing
              Type: main
ResultId 1