This meshing tech tip is perfect for when you really want to control the mesh through the whole volume or thickness of only a portion of a part. Mesh controls on a surface may not propagate through the entire thickness of the part, which in some cases may be necessary for accuracy. What you should do is use the Split feature!
You can create a multibody part from either a 2D sketch or a 3D surface as a "Trim Tool" for Insert > Features > Split. If you've already created a Simulation study, make sure you right-click on the study name and choose Update Components. This will update the component that you split with more than one body, and since they are probably the same material, you can just drag-and-drop the material from Body 1 to the rest of the bodies.
Apply a mesh control to one of the split bodies and you can control the mesh on that entire volume! Here is an example of a mesh control on a portion of a cube, where on the left it shows a compatible mesh and on the right an incompatible mesh. (Note: This example was not used for any real problem but just as a proof of concept for myself.)