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The polynomial-preserving recovery for higher order finite element methods in 2D and 3D

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  • The Polynomial-Preserving Recovery (PPR) technique is extended to recover continuous gradients from $C^0$ finite element solutions of an arbitrary order in 2D and 3D problems. The stability of the PPR is theoretically investigated in a general framework. In 2D, the stability is established under a simple geometric condition. The numerical experiments demonstrated that the PPR-recovered gradient enjoys superconvergence, and the Zienkiewicz-Zhu error estimator based on the PPR-recovered gradient is asymptotically exact.
    Mathematics Subject Classification: 65N30, 65N15, 65N12, 65D10,74S05, 41A10, 41A25.


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