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.

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 2010

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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10.1002/nla.694

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AU - Shu, Shi

AU - Chen, Long

AU - Xu, Jinchao

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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.

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

Abstract

All Science Journal Classification (ASJC) codes

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