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

Handle URI:
http://hdl.handle.net/10754/561859
Title:
Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials
Authors:
Huang, Yunqing; Li, Jichun; Yang, Wei; Sun, Shuyu ( 0000-0002-3078-864X )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computational Transport Phenomena Lab
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Sep-2011
DOI:
10.1016/j.jcp.2011.07.025
Type:
Article
ISSN:
00219991
Sponsors:
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.
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHuang, Yunqingen
dc.contributor.authorLi, Jichunen
dc.contributor.authorYang, Weien
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2015-08-03T09:32:40Zen
dc.date.available2015-08-03T09:32:40Zen
dc.date.issued2011-09en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2011.07.025en
dc.identifier.urihttp://hdl.handle.net/10754/561859en
dc.description.abstractNumerical 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.en
dc.description.sponsorshipPartially 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.en
dc.publisherElsevier BVen
dc.subjectMaxwell's equationsen
dc.subjectMetamaterialsen
dc.subjectMixed finite elementsen
dc.subjectSuperconvergenceen
dc.titleSuperconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterialsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionHunan Key Lab. for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, Hunan, Chinaen
dc.contributor.institutionDept. of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, United Statesen
kaust.authorSun, Shuyuen
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