An analytical characterization of the error in the measured equation of invariance

In previous publications, the authors have numerically shown that the measured equation of invariance (MEI) is not invariant to excitation. The major implication is that an appropriate set of metrons should be selected for each geometry and excitation in question. An argument, however, can be raised against these findings. One can claim that the MEI is indeed invariant, and that any discrepancies are entirely due to the mesh discretization error. The authors disprove this claim by a counterexample. They perform an analytical study of the MEI as applied to a perfectly conducting circular cylinder with a fixed choice of metrons. They then investigate the behavior of the MEI when the electrical radius of the cylinder becomes large and when the nodal separation goes to zero. They prove that even as the MEI residual goes to zero the error in the MEI solution remains finite and cannot be reduced below a certain limit.