In a recent electrostatic study, a plot of the peak electric field magnitude versus number of elements demonstrated a numerical overshoot. For coarse meshes, as mesh was refined, the peak electric field magnitude increased until a maximum was reached. Then as the mesh was refined, the peak electric field magnitude monotonically decreased until it reached a grid-independent value. What is the reason for this numerical overshoot? This problem was solved in ANSYS Maxwell and ANSYS tech support was unable to help. It's been too many years since I've studied numerical methods and I'm unfamiliar with numerical methods for electrostatics. Thank you very much for any information.
Although I am not an expert in Maxwell's Equations, the behaviour you describe is typical of high-order (non-monotone) schemes, when applied to nonsmooth solutions. This is not necessarily a mistake, and in fact it does not prevent the scheme from converging, as you noticed.
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