Abstract
In this paper, we develop the function, derivative and high-order derivatives recovery methods for the piecewise \(L^2\) projection and piecewise Lagrange interpolation. The presented recovery methods fully exploit the symmetry property to obtain the superconvergent recovered quantities. The analysis given here is based on Taylor expansion and to identify a symmetry sub-domain for superconvergence. Numerical examples are provided which demonstrate the superconvergence properties of the proposed recovery methods and its performance when applying to finite element method.
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Notes
The results of derivative recovery is the same as in [14], we present here for the reader’s convenience.
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Acknowledgements
Yi’s research was partially supported by NSFC Project (11671341), Hunan Provincial NSF Project (2015JJ2145) and Hunan Education Department Project (16A206). Huang’s research was partially supported by NSFC Project (91430213).
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Yi, N., Huang, Y. & Yang, W. Function, Derivative and High-Order Derivatives Recovery Methods Using the Local Symmetry Projection. J Sci Comput 74, 536–572 (2018). https://doi.org/10.1007/s10915-017-0451-6
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DOI: https://doi.org/10.1007/s10915-017-0451-6