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Zbl 0769.73084
Zienkiewicz, O.C.; Zhu, J.Z.
The superconvergent patch recovery and $a\ posteriori$ error estimates. I: The recovery technique. (English)
[J] Int. J. Numer. Methods Eng. 33, No.7, 1331-1364 (1992). ISSN 0029-5981

A general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes. The technique has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems. Numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent. One order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements. In particular, an $O(h\sp 4)$ convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time.

MSC 2000:: *74S05 Finite element methods
65N30 Finite numerical methods (BVP of PDE)
65N15 Error bounds (BVP of PDE)

Keywords: one order higher accuracy; linear elements; derivatives; quadratic and cubic elements; two order higher accuracy; quadratic triangular element

Cited in: Zbl 1215.65167 Zbl 1045.65098 Zbl 1169.74615 Zbl 0962.65095 Zbl 0941.74070 Zbl 0936.65132 Zbl 0949.74073 Zbl 0941.65116 Zbl 0858.65115 Zbl 0833.65119 Zbl 0811.65088 Zbl 0796.65125 Zbl 0778.73079 Zbl 0779.73078

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