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Hodge decomposition for two‐dimensional time‐harmonic Maxwell's equations: impedance boundary condition

We extend the Hodge decomposition approach for the cavity problem of two‐dimensional time‐harmonic Maxwell's equations to include the impedance boundary condition, with anisotropic electric permittivity and sign‐changing magnetic permeability. We derive error estimates for a P1 finite element method based on the Hodge decomposition approach and present results of numerical experiments that involve metamaterials and electromagnetic cloaking. The well‐posedness of the cavity problem when both electric permittivity and magnetic permeability can change sign is also discussed. Copyright © 2015 John Wiley & Sons, Ltd.