A Type of Finite Element Gradient Recovery Method based on Vertex-Edge-Face Interpolation: The Recovery Technique and Superconvergence Property
Qun Lin 1*, Hehu Xie 11 LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
Received 25 December 2010; Accepted (in revised version) 25 April 2011
Available online 27 July 2011
In this paper, a new type of gradient recovery method based on vertex-edge-face interpolation is introduced and analyzed. This method gives a new way to recover gradient approximations and has the same simplicity, efficiency, and superconvergence properties as those of superconvergence patch recovery method and polynomial preserving recovery method. Here, we introduce the recovery technique and analyze its superconvergence properties. We also show a simple application in the a posteriori error estimates. Some numerical examples illustrate the effectiveness of this recovery method.
AMS subject classifications: 65N30, 65N12, 65N15, 65D10, 74S05
Key words: Finite element method, least-squares fitting, vertex-edge-face interpolation, superconvergence, a posteriori error estimate.
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