the affine linear part actually needs the algebraic part of the riccati solution

[highlando]

it actually need $X_2 f_p$, where $f_p$ is the rhs of the (discrete) continuity equation.

For the driven cavity the BCs are 'divergence free' and thus $f_p=0$...

This may not hold for other setups.

[highlando]

maybe not, because it does not influence the differential part... ???

[highlando]

it does!!