Article
MSC:
35J25,
65D25,
65M60,
65N12,
65N30 | MR 2886235 | Zbl 1249.65258 | DOI: 10.1007/s10492-011-0030-3
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Keywords:
finite element method; derivative recovery technique; superconvergence and ultraconvergence; elliptic boundary problems; numerical examples
finite element method; derivative recovery technique; superconvergence and ultraconvergence; elliptic boundary problems; numerical examples
Summary:
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.
References:
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