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 interpolant $u_I$ 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.

Discovery of New Metastable Patterns in Diblock Copolymers - Volume 14 Issue 2 - Kai Jiang, Chu Wang, Yunqing Huang, Pingwen Zhang