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

Abstract In the present paper, we analyse in detail the spectral features of the matrix sequences arising from the Taylor–Hood $$\mathbb {P}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> - $$\mathbb {P}_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> 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.