Journal of Scientific Computing

, Volume 81, Issue 3, pp 1602–1629

# Superconvergent Recovery of Rectangular Edge Finite Element Approximation by Local Symmetry Projection

• Chao Wu
• Yunqing Huang
• Nianyu Yi
• Jinyun Yuan
Article

## Abstract

A new recovery method of rectangular edge finite element approximation for Maxwell’s equations is proposed by using the local symmetry projection. The recovery method is applied to the Nédélec interpolation to obtain the superconvergence of postprocessed Nédélec interpolation. Combining with the superclose result between the Nédélec interpolation and edge finite element approximation, it is shown that the postprocessed edge finite element solution superconverges to the exact solution. Numerical examples are presented to illustrate our theoretical analysis.

## Keywords

Maxwell’s equations Superconvergence Edge FEM Local symmetry projection

## Mathematics Subject Classification

65N15 65N30 65N50

## Notes

### Acknowledgements

Wu’s research was supported by NSFC Project (11801165, 11626099), Hunan Provincial Education Department Project (16C0636) and Pos-doc Jr. 407848/2017-7, CNPq, Brazil and Pos-doc 88887. 136371/2017-00, CAPEs, Brazil; Huang’s research was partially supported by NSFC Project (11826212, 11971410) and Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (2018WK4006); Yi’s research was partially supported by NSFC Project (11671341) and Hunan Provincial NSF Project (2019JJ20016); Yuan’s research was supported by CAPES and CNPq, Brazil.

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## Authors and Affiliations

• Chao Wu
• 1
• 3
• Yunqing Huang
• 2
• Nianyu Yi
• 2
Email author
• Jinyun Yuan
• 3
1. 1.School of Mathematics and Computational ScienceHunan University of Science and TechnologyXiangtanPeople’s Republic of China
2. 2.Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational ScienceXiangtan UniversityXiangtanPeople’s Republic of China
3. 3.Departamento de MatemáticaUniversidade Federal do Paraná, Centro PolitécnicoCuritibaBrazil