A posteriori error estimates are crucial ingredients in adaptive
finite element methods. An important class of error estimators is that
of estimators based on recovery techniques. In this talk, a polynomial
preserving recovery (PPR) method is proposed and analyzed. The method
is suitable for arbitrary meshes, especially meshes constructed from
the Delaunay triangulation. The method maintains the simplicity,
efficiency, and superconvergence property of the popular
Zienkiewicz-Zhu superconvergence patch recovery (SPR), and performs
better than SPR under certain meshes (such as the Chevron pattern) as
well as on boundaries. In fact, PPR is superconvergent for the Chevron
mesh and ultraconvergent at element edge centers for the regular
mesh. Some theoretical results will be given. In addition, numerical
comparison with SPR is also provided.
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