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<p>Unfitted mesh formulations for interface problems generally adopt two distinct methodologies: penalty-based approaches and explicit enrichment space techniques. While Stable Generalized Finite Element Method (SGFEM) has been rigorously established for lower-order elements, the construction of optimal enrichment spaces preserving approximation-theoretic properties within isogeometric analysis (IGA) frameworks remains an open challenge. In this paper, we introduce a stable quadratic generalized isogeometric analysis (SGIGA2) for two-dimensional elliptic interface problems. The method is achieved through two key ideas: a new quasi-interpolation for the function with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="366_2025_2138_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^0\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>0</mn> </msup> </math></EquationSource> </InlineEquation> continuous along interface and a new enrichment space with controlled condition number for the stiffness matrix. We mathematically prove that the present method has optimal convergence rates for elliptic interface problems and demonstrate its stability and robustness through numerical verification.</p>

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Stable quadratic generalized IsoGeometric analysis for elliptic interface problem

  • 期刊论文

  • 发表日期：

    2025年5月2日

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  • Yin Song,
  • Wenkai Hu,
  • Xin Li

摘要

Unfitted mesh formulations for interface problems generally adopt two distinct methodologies: penalty-based approaches and explicit enrichment space techniques. While Stable Generalized Finite Element Method (SGFEM) has been rigorously established for lower-order elements, the construction of optimal enrichment spaces preserving approximation-theoretic properties within isogeometric analysis (IGA) frameworks remains an open challenge. In this paper, we introduce a stable quadratic generalized isogeometric analysis (SGIGA2) for two-dimensional elliptic interface problems. The method is achieved through two key ideas: a new quasi-interpolation for the function with \(C^0\) C 0 continuous along interface and a new enrichment space with controlled condition number for the stiffness matrix. We mathematically prove that the present method has optimal convergence rates for elliptic interface problems and demonstrate its stability and robustness through numerical verification.