Superconvergent flux recovery of the Rannacher-Turek nonconforming element

10/23/2019

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by   Yuwen Li, et al.

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This work presents superconvergence estimates of the Rannacher-Turek element for second-order elliptic equations on any cubical meshes in R^2 and R^3. In particular, a recovered numerical flux is shown to be superclose to the Raviart-Thomas interpolant of the exact flux. We then design a superconvergent recovery operator based on local weighted averaging. Combining the supercloseness and the recovery operator, we prove that the recovered flux superconverges to the exact flux. As a by-product, we obtain a superconvergent recovery estimate of the Crouzeix-Raviart element method for general elliptic equations.