Abstract
A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite elements. Finally, some numerical examples are presented to illustrate the theoretical analysis.
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This work was supported in part by theNational Basic Research Program (2012CB955804) and the National Natural Science Foundation of China (11071033 and 11171251.
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Zhang, T., Zhang, S. Finite element derivative interpolation recovery technique and superconvergence. Appl Math 56, 513–531 (2011). https://doi.org/10.1007/s10492-011-0030-3
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DOI: https://doi.org/10.1007/s10492-011-0030-3