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factor 1/nu in K_p

Open nschloe opened this issue 7 years ago • 1 comments

The documentation says that the operator x1 is approximated by x2 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.

nschloe avatar Jun 28 '17 15:06 nschloe

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.

blechta avatar Jul 08 '18 18:07 blechta