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So I ran with my adjoint solver, but without a singularity on a sequence of refined meshes, and didn't see that behavior, as expected. My guess is as follows: If you think of the adjoint vector as a green's function, relating perturbations in the residual operator to a delta in the objective function (in this case weighted projections of pressure), I ...


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Generally, the viscosity we speak about (which is linked to the relax. time) is the kinematic viscosity $\nu$, not $\mu$ as you write. So, by replacing, you will find the right expression.


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