Superconvergence analysis of second and third order rectangular edge elements with applications to Maxwell’s equations

Abstract

Superconvergence for the second and third order edge elements is investigated on nonuniform rectangular meshes. First, we develop the explicit expression for the Nédélec interpolation based on the hierarchical basis functions. Then we prove that the pointwise interpolation error estimates are one order higher at element Gauss points than the standard analysis can provide. Using the superconvergence at Gauss points, we establish the discrete l2 norm superconvergence for the solution of Maxwell’s equations solved by both the second and third order rectangular edge elements. Numerical results justifying our theoretical analysis are presented.