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Superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes. For a large class of practically useful grids, the finite element solution u h is proven to be superclose to the inter-polant u I and as a result a postprocessing gradient recovery scheme for u h can be devised. The analysis is based on a number of carefully derived identities. In addition to its own theoretical interests, the result in this paper can be used for deriving asymptotically exact a posteriori error estimators for quadratic finite element methods.

Superconvergence of quadratic finite elements on mildly structured grids