ETA-PERCENT-SUPERCONVERGENCE OF FINITE-ELEMENT APPROXIMATIONS IN THE INTERIOR OF GENERAL MESHES OF TRIANGLES
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In this paper we introduce a new definition of superconvergence - tne %-superconvergence, which generalizes the classical idea of superconvergence to general meshes. We show that this new definition can be employed to determine the regions of least-error in any element in the interior of any grid by using a computer-based approach. We present numerical results for the standard displacement finite element method for the scalar equation of orthotropic heat-conduction, for meshes of conforming triangles of degree p, 1 p 5, and elements in the interior of the mesh. The results demonstrate that, unlike classical superconvergence, %-superconvergence is applicable to the complex grids which are employed in practical engineering computations. 1995.