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Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements


Authors: Zhiqiang Cai, Cuiyu He and Shun Zhang
Journal: Math. Comp. 86 (2017), 617-636
MSC (2010): Primary 65N30
DOI: https://doi.org/10.1090/mcom/3151
Published electronically: May 3, 2016
MathSciNet review: 3584542
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Abstract: In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach without using the Helmholtz decomposition. It is proved that the estimator is reliable with constant independent of the jump of diffusion coefficients across the interfaces, without the assumption that the diffusion coefficient is quasi-monotone. Numerical results for one test problem with intersecting interfaces are also presented.


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Additional Information

Zhiqiang Cai
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
Email: caiz@purdue.edu

Cuiyu He
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
Email: he75@purdue.edu

Shun Zhang
Affiliation: Department of Mathematics, City University of Hong Kong, Hong Kong
Email: shun.zhang@cityu.edu.hk

DOI: https://doi.org/10.1090/mcom/3151
Received by editor(s): July 17, 2014
Received by editor(s) in revised form: September 9, 2015
Published electronically: May 3, 2016
Additional Notes: This work was supported in part by the National Science Foundation under grants DMS-1217081 and DMS-1522707, the Purdue Research Foundation, and the Research Grants Council of the Hong Kong SAR, China, under the GRF Project No. 11303914, CityU 9042090.
Article copyright: © Copyright 2016 American Mathematical Society

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