Convergence of adaptive edge finite element methods for H(curl)-Elliptic problems

Liuqiang Zhong; Shi Shu; Long Chen; Jinchao Xu

doi:10.1002/nla.694

Convergence of adaptive edge finite element methods for H(curl)-Elliptic problems

Liuqiang Zhong, Shi Shu, Long Chen, Jinchao Xu

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

13 Scopus citations

Abstract

The standard adaptive edge finite element method (AEFEM), using first/second family Nédélec edge elements with any order, for the three-dimensional H(curl)-elliptic problems with variable coefficients is shown to be convergent for the sum of the energy error and the scaled error estimator. The special treatment of the data oscillation and the interior node property are removed from the proof. Numerical experiments indicate that the adaptive meshes and the associated numerical complexity are quasi-optimal. © 2010 John Wiley & Sons, Ltd.

Original language	English (US)
Pages (from-to)	415-432
Number of pages	18
Journal	Numerical Linear Algebra with Applications
Volume	17
Issue number	2-3
DOIs	https://doi.org/10.1002/nla.694
State	Published - Apr 1 2010
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1002/nla.694

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abstract = "The standard adaptive edge finite element method (AEFEM), using first/second family N{\'e}d{\'e}lec edge elements with any order, for the three-dimensional H(curl)-elliptic problems with variable coefficients is shown to be convergent for the sum of the energy error and the scaled error estimator. The special treatment of the data oscillation and the interior node property are removed from the proof. Numerical experiments indicate that the adaptive meshes and the associated numerical complexity are quasi-optimal. {\textcopyright} 2010 John Wiley & Sons, Ltd.",

author = "Liuqiang Zhong and Shi Shu and Long Chen and Jinchao Xu",

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T1 - Convergence of adaptive edge finite element methods for H(curl)-Elliptic problems

AU - Zhong, Liuqiang

AU - Shu, Shi

AU - Chen, Long

AU - Xu, Jinchao

N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15

PY - 2010/4/1

Y1 - 2010/4/1

N2 - The standard adaptive edge finite element method (AEFEM), using first/second family Nédélec edge elements with any order, for the three-dimensional H(curl)-elliptic problems with variable coefficients is shown to be convergent for the sum of the energy error and the scaled error estimator. The special treatment of the data oscillation and the interior node property are removed from the proof. Numerical experiments indicate that the adaptive meshes and the associated numerical complexity are quasi-optimal. © 2010 John Wiley & Sons, Ltd.

AB - The standard adaptive edge finite element method (AEFEM), using first/second family Nédélec edge elements with any order, for the three-dimensional H(curl)-elliptic problems with variable coefficients is shown to be convergent for the sum of the energy error and the scaled error estimator. The special treatment of the data oscillation and the interior node property are removed from the proof. Numerical experiments indicate that the adaptive meshes and the associated numerical complexity are quasi-optimal. © 2010 John Wiley & Sons, Ltd.

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JO - Numerical Linear Algebra with Applications

JF - Numerical Linear Algebra with Applications

IS - 2-3

ER -

Convergence of adaptive edge finite element methods for H(curl)-Elliptic problems

Abstract

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ASJC Scopus subject areas

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