### Abstract

Original language | English |
---|---|

Pages (from-to) | 471-493 |

Number of pages | 22 |

Journal | Philosophical Transactions A: Mathematical, Physical and Engineering Sciences |

Volume | 362 |

Issue number | 1816 |

DOIs | |

Publication status | Published - Mar 2004 |

### Fingerprint

### Keywords

- edge finite element
- numerical dispersion
- discrete dispersion relation

### Cite this

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*Philosophical Transactions A: Mathematical, Physical and Engineering Sciences*, vol. 362, no. 1816, pp. 471-493. https://doi.org/10.1098/rsta.2003.1331

**Dispersive properties of high order nedelec/edge element approximation of the time-harmonic Maxwell equations.** / Ainsworth, Mark.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dispersive properties of high order nedelec/edge element approximation of the time-harmonic Maxwell equations

AU - Ainsworth, Mark

PY - 2004/3

Y1 - 2004/3

N2 - The dispersive behaviour of high-order Næ#169;dæ#169;lec element approximation of the time harmonic Maxwell equations at a prescribed temporal frequency ω on tensor-product meshes of size h is analysed. A simple argument is presented, showing that the discrete dispersion relation may be expressed in terms of that for the approximation of the scalar Helmholtz equation in one dimension. An explicit form for the one-dimensional dispersion relation is given, valid for arbitrary order of approximation. Explicit expressions for the leading term in the error in the regimes where ωh is small, showing that the dispersion relation is accurate to order 2p for a pth-order method; and in the high-wavenumber limit where 1«ωh, showing that in this case the error reduces at a super-exponential rate once the order of approximation exceeds a certain threshold, which is given explicitly.

AB - The dispersive behaviour of high-order Næ#169;dæ#169;lec element approximation of the time harmonic Maxwell equations at a prescribed temporal frequency ω on tensor-product meshes of size h is analysed. A simple argument is presented, showing that the discrete dispersion relation may be expressed in terms of that for the approximation of the scalar Helmholtz equation in one dimension. An explicit form for the one-dimensional dispersion relation is given, valid for arbitrary order of approximation. Explicit expressions for the leading term in the error in the regimes where ωh is small, showing that the dispersion relation is accurate to order 2p for a pth-order method; and in the high-wavenumber limit where 1«ωh, showing that in this case the error reduces at a super-exponential rate once the order of approximation exceeds a certain threshold, which is given explicitly.

KW - edge finite element

KW - numerical dispersion

KW - discrete dispersion relation

U2 - 10.1098/rsta.2003.1331

DO - 10.1098/rsta.2003.1331

M3 - Article

VL - 362

SP - 471

EP - 493

JO - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 1816

ER -