Ensure Elements Have Interior Vertices
Ensure elements have interior vertices modifies the mesh to ensure that it has at least one vertex in the interior.
There are several options that can be selected from the drop down list. For example, if Face is selected, it will modify the mesh so that the interior face has at least one vertex in the interior. Similarly if Face And Region is selected, it will modify the mesh so that interior faces and regions have at least one vertex in the interior, but interior edges could very well have both vertices on the boundary. Boundary layer and extrusion mesh entities will not be modified by this option.