A new family of nonconforming elements with H(curl)-continuity for the three-dimensional quad-curl problem
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We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem. The proposed finite element spaces are subspaces of H(curl), but not of H(grad curl), which are different from the existing nonconforming ones. The well-posedness of the discrete problem is proved and optimal error estimates in discrete H(grad curl) norm, H(curl) norm and L^2 norm are derived. Numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.
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