Geodesic
Finite element derivative interpolation recovery technique and superconvergence
Applications of Mathematics, Tome 56 (2011) no. 6, pp. 513-531.

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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.
DOI : 10.1007/s10492-011-0030-3
Classification : 35J25, 65D25, 65M60, 65N12, 65N30
Keywords: finite element method; derivative recovery technique; superconvergence and ultraconvergence; elliptic boundary problems; numerical examples 
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     title = {Finite element derivative interpolation recovery technique and superconvergence},
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     pages = {513--531},
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Zhang, Tie; Zhang, Shuhua. Finite element derivative interpolation recovery technique and superconvergence. Applications of Mathematics, Tome 56 (2011) no. 6, pp. 513-531. doi : 10.1007/s10492-011-0030-3. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0030-3/

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