[For part I, see Math. Models Methods Appl. Sci. 8, No. 5, 787–820 (1998; Zbl 0958.76048).
Summary: We analyze the divergence stability of mixed \(hp\) finite element methods for incompressible fluid flows. A discrete inf-sup condition is proved for a general class of meshes. The meshes may be refined anisotropically, geometrically, and may contain hanging nodes on geometric patches. The inf-sup constant is shown to be independent of the aspect ratio of the anisotropic elements, and the dependence on the polynomial degree is analyzed. Numerical estimates of inf-sup constants confirm the theoretical results.