What block preconditioners really do

And one final remark: They way your Multigrid is programmed, you are only solving on the lowest order DOFs. Prolongations only transfer lowest order DOFs, so you need your smoother on the finest level to take care of the high order part by itself. But, the smoother blocks you are using are just one block for each vertex, consisting of the single lowest order DOF for that vertex.

Hope this helps,
Best,
Lukas

Thank you very much, Lukas.

Now I understand the problem. The way the multiplication is coded, changes not only rho but also res !

As for your second remark, I used on purpose only lowest order smoother in the minimal example. In the code, I have a higher order smoother on the finest mesh.

Best and thank you once more,
Jan