View in EDS

A least-squares virtual element method on polytopal mesh for a curl-div system.

Saved in:
Bibliographic Details
Title: A least-squares virtual element method on polytopal mesh for a curl-div system.
Authors: Duan, Huoyuan1 (AUTHOR) hyduan.math@whu.edu.cn, Zhu, Duowei1,2 (AUTHOR) dwzhu.cherry@whu.edu.cn
Source: Journal of Computational & Applied Mathematics. Aug2026, Vol. 481, pN.PAG-N.PAG. 1p.
Subjects: Magnetostatics, Least squares, Polytopes, Finite element method, Numerical calculations, Error analysis in mathematics, Orthogonal decompositions
Abstract: A new virtual element method of least-squares type is proposed for numerically solving a curl-div system, which typically arises from the magnetostatic problem. We employ the nodal virtual elements on polytopal meshes. With the Helmholtz L 2-orthogonal decomposition and the related regular-singular decomposition, we develop a rigorous argument for proving the L 2-coercivity. For the k (k ≥ 1) order virtual element which has the degrees of freedom in the interiors of the element faces, we strictly establish the optimal error estimates O (hr) for the singular solution which has a low regularity and only belongs to (Hr (Ω)) d , d = 2 , 3 , for 1/2 < r < 1. For higher-order regularity solution, L 2-norm O (h k + 1) optimal convergence can hold for k ≥ 1. Numerical results are provided. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational & Applied 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
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 191294394
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: A least-squares virtual element method on polytopal mesh for a curl-div system.
– Name: Author
  Label: Authors
  Group: Au
  Data: &lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Duan%2C+Huoyuan%22&quot;&gt;Duan, Huoyuan&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt; (AUTHOR)&lt;i&gt; hyduan.math@whu.edu.cn&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Zhu%2C+Duowei%22&quot;&gt;Zhu, Duowei&lt;/searchLink&gt;&lt;relatesTo&gt;1,2&lt;/relatesTo&gt; (AUTHOR)&lt;i&gt; dwzhu.cherry@whu.edu.cn&lt;/i&gt;
– Name: TitleSource
  Label: Source
  Group: Src
  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Journal+of+Computational+%26+Applied+Mathematics%22&quot;&gt;Journal of Computational &amp; Applied Mathematics&lt;/searchLink&gt;. Aug2026, Vol. 481, pN.PAG-N.PAG. 1p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: &lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Magnetostatics%22&quot;&gt;Magnetostatics&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Least+squares%22&quot;&gt;Least squares&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Polytopes%22&quot;&gt;Polytopes&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Finite+element+method%22&quot;&gt;Finite element method&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Numerical+calculations%22&quot;&gt;Numerical calculations&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Error+analysis+in+mathematics%22&quot;&gt;Error analysis in mathematics&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Orthogonal+decompositions%22&quot;&gt;Orthogonal decompositions&lt;/searchLink&gt;
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A new virtual element method of least-squares type is proposed for numerically solving a curl-div system, which typically arises from the magnetostatic problem. We employ the nodal virtual elements on polytopal meshes. With the Helmholtz L 2-orthogonal decomposition and the related regular-singular decomposition, we develop a rigorous argument for proving the L 2-coercivity. For the k (k ≥ 1) order virtual element which has the degrees of freedom in the interiors of the element faces, we strictly establish the optimal error estimates O (hr) for the singular solution which has a low regularity and only belongs to (Hr (Ω)) d , d = 2 , 3 , for 1/2 &lt; r &lt; 1. For higher-order regularity solution, L 2-norm O (h k + 1) optimal convergence can hold for k ≥ 1. Numerical results are provided. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: &lt;i&gt;Copyright of Journal of Computational &amp; Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder&#39;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.&lt;/i&gt; (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=191294394
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.cam.2025.117275
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Magnetostatics
        Type: general
      – SubjectFull: Least squares
        Type: general
      – SubjectFull: Polytopes
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Numerical calculations
        Type: general
      – SubjectFull: Error analysis in mathematics
        Type: general
      – SubjectFull: Orthogonal decompositions
        Type: general
    Titles:
      – TitleFull: A least-squares virtual element method on polytopal mesh for a curl-div system.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Duan, Huoyuan
      – PersonEntity:
          Name:
            NameFull: Zhu, Duowei
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 03770427
          Numbering:
            – Type: volume
              Value: 481
          Titles:
            – TitleFull: Journal of Computational & Applied Mathematics
              Type: main
ResultId 1