Developing and Analyzing Some Novel Finite Element Schemes for the Electromagnetic Rotation Cloak Model

One potential application of metamaterials is for designing invisibility cloaks. In this paper, we are interested in a rotation cloak model. Here we carry out the mathematical analysis of this model for the first time. Through a careful analysis, we reformulate a new system of governing partial differential equations by reducing one unknown variable from the originally developed modeling equations in Yang et al. (Commun Comput Phys 25:135–154, 2019). Then some novel finite element schemes are proposed and their stability and optimal error estimate are proved. Numerical simulations are presented to demonstrate that the new schemes for the reduced modeling equations can effectively reproduce the rotation cloaking phenomenon.