While answering one of the questions on meshing process, I encountered a lack of understanding on my end for the comparison of the mesh quality.
First, consider an unstructured mesh created in GMSH for a 2-D shape (I am not interested in this particular shape, just here for the illustration). The elements are controlled only through the characteristic length, which basically dictates, how many elements are created along the geometry boundaries.
Now, I can detect the regions in the mesh that are "kind of suitable" for a structured mesh. That could be done automatically, say, using marching cubes.
Now, both meshes satisfy the original criteria for the size of the element. But the second mesh has a lot of elements that are exactly the same - allowing for significant savings in the required amount of computations while featuring a similar number of triangular elements (even a little bit less).
Is the second mesh bad in general? Does a lot depend on the kind of basis functions that will be used?
Now, I am particularly interested in using the meshes in frequency-domain computational electromagnetics, where the common meshing is done at $\lambda/10$, $\lambda$ is the wavelength. Say, both meshes satisfy $\lambda/10$ requirement (largest triangular edge is smaller than $\lambda/10$). Is there something fundamentally bad by using this type of a hybrid structured/unstructured mesh?
NB: I am usually using integral-equation methods; however, don't mind having an understanding of what happens, in general, and for FEM and others, in particular.