HFSS - Mesh at the center and the edge of surface

Using "On selection" "Length Based" feature of the "Assign Mesh Operation" one can improve the meshing on the surface. Very nice feature, but the mesh is fairly equal on the whole surface (center and edges).

What I would like to do is to improve the mesh on the edges of the surface (where current concentrates), but not so much in the center.

What are the options to improve the mesh on the edges, but not in the center of the surface?

Spliting the surface to ribbons/strips at the edges is one way, but is there a quicker way?