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Journal of Scientific Computing

Erschienen in:

01.04.2020

Robust Equilibrated Error Estimator for Diffusion Problems: Mixed Finite Elements in Two Dimensions

verfasst von: Difeng Cai, Zhiqiang Cai, Shun Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2020

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Abstract

This paper introduces and analyzes an equilibrated a posteriori error estimator for mixed finite element approximations to the diffusion problem in two dimensions. The estimator, which is a generalization of those in Braess and Schöberl (Math Comput 77:651–672, 2008) and Cai and Zhang (SIAM J Numer Anal 50(1):151–170, 2012), is based on the Prager–Synge identity and on a local recovery of a gradient in the curl free subspace of the \(H(\text {curl})\)-confirming finite element spaces. The resulting estimator admits guaranteed reliability, and its robust local efficiency is proved under the quasi-monotonicity condition of the diffusion coefficient. Numerical experiments are given to confirm the theoretical results.

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Titel: Robust Equilibrated Error Estimator for Diffusion Problems: Mixed Finite Elements in Two Dimensions
verfasst von: Difeng Cai
Zhiqiang Cai
Shun Zhang
Publikationsdatum: 01.04.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01199-9

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