Eta%-Superconvergence in the Interior of Locally Refined Meshes ofQuadrilaterals: Superconvergence of the Gradient in Finite Element Solutions of Laplace's and Poisson's Equations

摘要

This paper is the third in a series in which we study the superconvergence offinite element solutions by a computer-based approach. We studied classical superconvergence and we introduced the new concept of eta%-superconvergence and showed that it can be employed to determine regions of least-error for the derivatives of the finite element solution in the interior of any grid of triangular elements. Here we use the same ideas to study the superconvergence of the derivatives of the finite element solution in the interior of complex grids of quadrilaterals of the type used in practical computations.