A posteriori error estimators for the first-order least-squares finite element method

Jaeun Ku; Eun Jae Park

doi:10.1016/j.cam.2010.06.004

A posteriori error estimators for the first-order least-squares finite element method

Jaeun Ku, Eun Jae Park

Department of Computational Science and Engineering

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

5 Citations (Scopus)

Abstract

In this paper, we propose a posteriori error estimators for certain quantities of interest for a first-order least-squares finite element method. In particular, we propose an a posteriori error estimator for when one is interested in ||σ-σ_h||₀ where σ=-A∇u. Our a posteriori error estimators are obtained by assigning proper weight (in terms of local mesh size hT) to the terms of the least-squares functional. An a posteriori error analysis yields reliable and efficient estimates based on residuals. Numerical examples are presented to show the effectivity of our error estimators.

Original language	English
Pages (from-to)	293-300
Number of pages	8
Journal	Journal of Computational and Applied Mathematics
Volume	235
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2010.06.004
Publication status	Published - 2010 Nov 1

Bibliographical note

Funding Information:
The research of EJP was supported in part by the Korea Research Foundation KRF-2007-314-C00084 and the WCU program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( R31-2008-000-10049-0 ).

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2010.06.004

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abstract = "In this paper, we propose a posteriori error estimators for certain quantities of interest for a first-order least-squares finite element method. In particular, we propose an a posteriori error estimator for when one is interested in ||σ-σh||0 where σ=-A∇u. Our a posteriori error estimators are obtained by assigning proper weight (in terms of local mesh size hT) to the terms of the least-squares functional. An a posteriori error analysis yields reliable and efficient estimates based on residuals. Numerical examples are presented to show the effectivity of our error estimators.",

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AB - In this paper, we propose a posteriori error estimators for certain quantities of interest for a first-order least-squares finite element method. In particular, we propose an a posteriori error estimator for when one is interested in ||σ-σh||0 where σ=-A∇u. Our a posteriori error estimators are obtained by assigning proper weight (in terms of local mesh size hT) to the terms of the least-squares functional. An a posteriori error analysis yields reliable and efficient estimates based on residuals. Numerical examples are presented to show the effectivity of our error estimators.

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A posteriori error estimators for the first-order least-squares finite element method

Abstract

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