Spectral analysis of the stiffness matrix sequence in the approximated Stokes equation
Provides theoretical spectral analysis for a specific finite element discretization of the Stokes problem, which is incremental for researchers working on preconditioning of such systems.
The paper analyzes the spectral properties of stiffness matrix sequences from the Taylor-Hood approximation of the 2D Stokes problem with variable viscosity, providing localization and distributional results supported by numerical tests.
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.