Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

Yunqing Huang, Jichun Li, Wei Yang, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.
Original languageEnglish (US)
Pages (from-to)8275-8289
Number of pages15
JournalJournal of Computational Physics
Volume230
Issue number22
DOIs
StatePublished - Sep 2011

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Partially supported by the NSFC Key Project 11031006 and Hunan Provincial NSF Project 10JJ7001.Supported by National Science Foundation Grant DMS-0810896.Supported by Hunan Education Department Key Project 10A117.Supported by KAUST Faculty Baseline Research Fund.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

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