Dear Michal,

You mean because once you apply an inhomogeneous Dirichlet condition on the velocity you also get a contribution because the divergence is not zero? You could work around that by applying a function in the whole domain that satisfies the Dirichlet constraints and is divergence free, in which case you should not get a contribution to right right hand side of the divergence equation but only the momentum equation. On the other hand, I'm not sure how easy it would be to construct such a function...

Regarding the workaround: It could work by the modification you suggested, but we cannot really fix that in the library because the operators are meant for linear operators and not affine ones. The problematic issue is that there are some cases where you want to apply an operator with a non-zero constraint and others where you don't. For example, all Krylov solvers expect you to provide a matrix-vector for the linear operator, not the affine one as you would get when you have inhomogeneous constraints inside the mat-vec. In particular, I do not really understand the part in your second post where you talk about the vmult_interface_{up,down} functions because those are only used for multigrid where the library always assumes to work on homogeneous problems.

I have not gone down this route and as far as I know, nobody else has previously - including the matrix-based solvers we have available in deal.II whose way of operation resembles the setup I described in my previous post, but do it inside the ConstraintMatrix::distribute_local_to_global call - so I cannot say how much work that would be. We would be happy to provide a solution that is generic if you find one, but I'm not sure I will be able to help much along this direction.

Best,
Martin

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