I have found the solution to some extent: the permissible ratio of the height of the element in the inflation layer over is width is controlled with a "Maximum height over base" parameter in the global mesh inflation group under the advanced settings.

The maximum is 5 and it didn't solve it completely. Increasing the Total Thickness of the inflation on the problematic face also did not help to completely equalize the thickness of the layers near the corner. Only decreasing the thickness elsewhere helped to achieve what I wanted (here I also used twice less elements across the gap than in the initial post):

Corrected inflation layer thickness in the corner. Skeweness colormap.


However now I have a problem which I left out in my initial question: the tetrahedral mesh in that corner has few elements of a very poor quality (the colormap in the pic is a Skeweness). I have no clear vision how to improve it and just tweak global sizing parameters as well as playing with element size on the adjacent faces. Can anyone suggest any ideas which way to go, which parameters to focus on to improve these few tetrahedrons in the corner?

Note that they are also quite long in the direction into the page which is dictated by the mesh on that small face. Should I create a separate discussion for this question?

I would still welcome any suggestions, If there are, on if there is a better way to control the layer thickness, than I did.

Thank you