fenapack
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factor 1/nu in K_p
The documentation says that the operator
is approximated by
It's not immediately obvious why there should be a factor
1 / nu
in K_p
. Is this correct? If yes, it probably warrants a little more explanation.
Well,
X^{-1} = ( -\nu \Delta + \mathbf{v} \cdot \nabla ) ( - \Delta )^{-1}
= \nu ( I + \nu^{-1} \mathbf{v} \cdot \nabla ( -\Delta )^{-1} )
When you add at the appropriate place the mass matrix solve, which is the Riesz map from (L^2)^*
to L^2
and is customarily not written explicitly in infinite-dimensional formulas, you get the matrix formula.
I agree that the documentation could be more clear about that.