Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes

Mark Ainsworth; Joe Coyle

doi:10.1016/S0045-7825(01)00259-6

Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes

Mark Ainsworth, Joe Coyle

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

74 Citations (Scopus)

Abstract

We construct and study a set of hierarchic basis functions for the Galerkin discretisation of the space H(curl;Φ#169;) suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non-uniform order polynomial approximation. We investigate the conditioning and dispersive behaviour of the elements. In addition, numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time-harmonic Maxwell's equations that have singularities.

Original language	English
Pages (from-to)	6709-6733
Number of pages	24
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	190
Issue number	49-50
DOIs	https://doi.org/10.1016/S0045-7825(01)00259-6
Publication status	Published - 12 Oct 2001

Keywords

Time-harmonic Maxwell's equations
Computational electromagnetism
Hierarchic edge elements
Hybrid meshes

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10.1016/S0045-7825(01)00259-6

http://dx.doi.org/10.1016/S0045-7825(01)00259-6

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Cite this

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abstract = "We construct and study a set of hierarchic basis functions for the Galerkin discretisation of the space H(curl;Φ#169;) suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non-uniform order polynomial approximation. We investigate the conditioning and dispersive behaviour of the elements. In addition, numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time-harmonic Maxwell's equations that have singularities.",

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AU - Coyle, Joe

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N2 - We construct and study a set of hierarchic basis functions for the Galerkin discretisation of the space H(curl;Φ#169;) suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non-uniform order polynomial approximation. We investigate the conditioning and dispersive behaviour of the elements. In addition, numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time-harmonic Maxwell's equations that have singularities.

AB - We construct and study a set of hierarchic basis functions for the Galerkin discretisation of the space H(curl;Φ#169;) suitable for hybrid meshes containing both quadrilateral and triangular elements with arbitrary non-uniform order polynomial approximation. We investigate the conditioning and dispersive behaviour of the elements. In addition, numerical examples are shown which demonstrate the accuracy of the space for computing solutions of the time-harmonic Maxwell's equations that have singularities.

KW - Time-harmonic Maxwell's equations

KW - Computational electromagnetism

KW - Hierarchic edge elements

KW - Hybrid meshes

UR - http://dx.doi.org/10.1016/S0045-7825(01)00259-6

U2 - 10.1016/S0045-7825(01)00259-6

DO - 10.1016/S0045-7825(01)00259-6

M3 - Article

VL - 190

SP - 6709

EP - 6733

JO - Computer Methods in Applied Mechanics end Engineering

JF - Computer Methods in Applied Mechanics end Engineering

SN - 0045-7825

IS - 49-50

ER -