ETA-PERCENT-SUPERCONVERGENCE IN THE INTERIOR OF LOCALLY REFINED MESHES OF QUADRILATERALS - SUPERCONVERGENCE OF THE GRADIENT IN FINITE-ELEMENT SOLUTIONS OF LAPLACE AND POISSON EQUATIONS

This paper is the third in a series in which we study the superconverg ence of finite element solutions by a computer-based approach. In [1] we studied classical superconvergence and in [2] we introduced the new concept of eta%-superconvergence and showed that it can be employed t o determine regions of least error for the derivatives of the finite e lement solution in the interior of any grid of triangular elements. He re we use the same ideas to study the superconvergence of the derivati ves of the finite element solution in the interior of complex grids of quadrilaterals of the type used in practical computations.