In this paper we introduce a new definition of superconvergence - tne η%-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, η%-superconvergence is applicable to the complex grids which are employed in practical engineering computations. © 1995.