Superconvergence of a nonconforming brick element for the quad-curl problem

09/05/2023

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by   Xinchen Zhou, et al.

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This short note shows the superconvergence of an H(grad curl)-nonconforming brick element very recently introduced in [17] for the quad-curl problem. The supercloseness is based on proper modifications for both the interpolation and the discrete formulation, leading to an O(h^2) superclose order in the discrete H(grad curl) norm. Moreover, we propose a suitable postprocessing method to ensure the global superconvergence. Numerical results verify our theory.