The exact construction is a restatement of known irrotational-flow solutions, and the numerical method is a fitted approximation with no proven contraction.
Botelho, Functional Analysis and Applied Optimizati on in Banach Spaces, Springer Switzerland, 2014
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On the generalized method lines applied to the time-independent incompressible Navier-Stokes system
The exact construction is a restatement of known irrotational-flow solutions, and the numerical method is a fitted approximation with no proven contraction.