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arXiv · 2510.25252

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

Samuele Ferri·Chiara Giraudo·Valerio Loi·Miroslav Kuchta·Stefano Serra-Capizzano
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Abstract

In the present paper, we analyze in detail the spectral features of the matrix sequences arising from the Taylor-Hood $\mathbb{P}_2$-$\mathbb{P}_1$ approximation of variable viscosity for $2d$ 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.

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Samuele Ferri, Chiara Giraudo, Valerio Loi, Miroslav Kuchta, Stefano Serra-Capizzano. 2025-10-29. Spectral analysis of the stiffness matrix sequence in the approximated Stokes equation. https://arxiv.org/abs/2510.25252

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