### Abstract

We consider a standard Adaptive Edge Finite Element Method (AEFEM) based on arbitrary order Nédélec edge elements, for three-dimensional indefinite time-harmonic Maxwell equations. We prove that the AEFEM gives a contraction for the sum of the energy error and the scaled error estimator, between two consecutive adaptive loops provided the initial mesh is fine enough. Using the geometric decay, we show that the AEFEM yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom. The main technical contribution of the paper is the establishment of a quasi-orthogonality and a localized a posteriori error estimator.

Original language | English (US) |
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Pages (from-to) | 623-642 |

Number of pages | 20 |

Journal | Mathematics of Computation |

Volume | 81 |

Issue number | 278 |

DOIs | |

State | Published - Mar 30 2012 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Mathematics of Computation*,

*81*(278), 623-642. https://doi.org/10.1090/S0025-5718-2011-02544-5