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<p>In the present paper, we analyse in detail the spectral features of the matrix sequences arising from the Taylor–Hood <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {P}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">P</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {P}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">P</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> approximation of variable viscosity for the 2D Stokes problem under weak assumptions on the regularity of the diffusion. Localization and distributional spectral results are provided, accompanied by numerical tests and visualizations. A preliminary study of the impact of our findings on the preconditioning problem is also presented. A final section with concluding remarks and open problems ends the current work.</p>

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Spectral analysis of the stiffness matrix sequence in the approximated Stokes equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月30日

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  • Samuele Ferri,
  • Chiara Giraudo,
  • Valerio Loi,
  • Miroslav Kuchta,
  • Stefano Serra-Capizzano

摘要

In the present paper, we analyse in detail the spectral features of the matrix sequences arising from the Taylor–Hood \(\mathbb {P}_2\) P 2 - \(\mathbb {P}_1\) P 1 approximation of variable viscosity for the 2D Stokes problem under weak assumptions on the regularity of the diffusion. Localization and distributional spectral results are provided, accompanied by numerical tests and visualizations. A preliminary study of the impact of our findings on the preconditioning problem is also presented. A final section with concluding remarks and open problems ends the current work.