Superconvergence recovery of cubic edge elements for Maxwell's equations

In this article, a new recovery method is designed and analyzed for curl conforming elements on cuboid mesh. The proposed recovery method fully exploits the potential of symmetry to obtain the superconvergence of recovered edge finite element solution in discrete L-2 norm. The idea is to identify a symmetry sub-domain such that a polynomial of the same degree is recovered by local L-2 projection, based on which the recovered values follow. Combined with extrapolation and the least square fitting for the linear edge elements and quadratic edge elements, respectively, we obtain global superconvergence for recovered quantities in L-2 norm. Numerical experiments are provided to validate our theoretical findings. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This article introduces a new recovery method for curl conforming elements on cuboid mesh, achieving superconvergence of recovered edge finite element solution by exploiting symmetry. Theoretical findings are validated through numerical experiments.