Discrete and Continuous Dynamical Systems - B · 2005 · 67 citations · 17 references
ComputingComputational EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisError EstimationFinite Element DiscretizationFinite Element FormulationNumerical AlgorithmsNumerical StabilityError Estimation For Finite Element SolutionsHigh-order Finite ElementsHigher-order Finite ElementsZienkiewicz-zhu Error Estimator
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.
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