Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems

Difeng Cai; Zhiqiang Cai; Shun Zhang

doi:10.1007/s00211-019-01075-1

Author(s)

Difeng Cai
Zhiqiang Cai
Shun Zhang

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	1-21
Journal / Publication	Numerische Mathematik
Volume	144
Issue number	1
Online published	10 Oct 2019
Publication status	Published - Jan 2020

Link(s)

DOI	DOI https://doi.org/10.1007/s00211-019-01075-1 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85074493700&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(51569f28-8015-4bd9-b028-fd4de90e329a).html

Abstract

We present a patch-based equilibrated flux recovery procedure for the conforming finite element approximation to diffusion problems. The recovered flux is computed as the solution to a local constraint-free minimization problem on each patch. The approach is valid for higher order conforming elements in both two and three dimensions. The resulting estimator admits guaranteed reliability and the robust local efficiency is proved under the quasi-monotonicity condition of the diffusion coefficient. Numerical experiments are given to confirm the theoretical results.

Citation Format(s)

[ RIS ] [ BibTeX ]

Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. / Cai, Difeng; Cai, Zhiqiang; Zhang, Shun.

In: Numerische Mathematik, Vol. 144, No. 1, 01.2020, p. 1-21.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Cai, D, Cai, Z & Zhang, S 2020, 'Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems', Numerische Mathematik, vol. 144, no. 1, pp. 1-21. https://doi.org/10.1007/s00211-019-01075-1

Cai, D., Cai, Z., & Zhang, S. (2020). Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Numerische Mathematik, 144(1), 1-21. https://doi.org/10.1007/s00211-019-01075-1

Cai D, Cai Z, Zhang S. Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. Numerische Mathematik. 2020 Jan;144(1):1-21. Epub 2019 Oct 10. doi: 10.1007/s00211-019-01075-1

Cai, Difeng ; Cai, Zhiqiang ; Zhang, Shun. / Robust equilibrated a posteriori error estimator for higher order finite element approximations to diffusion problems. In: Numerische Mathematik. 2020 ; Vol. 144, No. 1. pp. 1-21.