l2 superconvergence analysis of nonconforming element approximation for 3D time-harmonic Maxwell's equations

In this paper, the superconvergent property is found for the interpolation error of the nonconforming finite element at element centers. Based upon this property, the superconvergence results in the discrete l2 norm for the solutions E→,H→ and curl→E→ are presented for the 3D time-harmonic Maxwell's equations. In order to get the global superconvergence, a new postprocess operator derived from the rotated Q1 element interpolation is constructed, which is based on the superconvergence points. All theoretical results are justified by the provided smoothing and non-smoothing numerical tests.