Scholarlink

<p>This paper presents an interior penalty discontinuous Galerkin (IPDG) method using the local orthogonal decomposition (LOD) technique to solve the multiscale elliptic problems with highly varying coefficients. The key idea of this method is to construct a special cell problem corrector term under the elliptic projection operator, and then incorporate it into the coarse scale space, ensuring that the numerical solution space has good <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3301_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> approximation property. Through this approach, the proposed method effectively eliminates the influence of the pollution factor and results in smaller patches for the localization problems. The error analysis is performed for highly varying coefficients without any assumptions on scale separation or periodicity. Numerical experiments with periodic and random highly varying coefficients, as well as multiscale problems involving thin conductivity channels, are provided to verify the efficiency and accuracy of the proposed method.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An IPDG multiscale method based on the LOD technique for elliptic problems with highly varying coefficients

  • 期刊论文

  • 发表日期：

    2025年7月7日

查看全文
  • Kuokuo Zhang,
  • Fei Song

摘要

This paper presents an interior penalty discontinuous Galerkin (IPDG) method using the local orthogonal decomposition (LOD) technique to solve the multiscale elliptic problems with highly varying coefficients. The key idea of this method is to construct a special cell problem corrector term under the elliptic projection operator, and then incorporate it into the coarse scale space, ensuring that the numerical solution space has good \(H^1\) H 1 approximation property. Through this approach, the proposed method effectively eliminates the influence of the pollution factor and results in smaller patches for the localization problems. The error analysis is performed for highly varying coefficients without any assumptions on scale separation or periodicity. Numerical experiments with periodic and random highly varying coefficients, as well as multiscale problems involving thin conductivity channels, are provided to verify the efficiency and accuracy of the proposed method.