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

Cai, Zhiqiang; He, Cuiyu; Zhang, Shun

doi:10.1090/mcom/3151

Residual-based a posteriori error estimate for interface problems: Nonconforming linear elements
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by Zhiqiang Cai, Cuiyu He and Shun Zhang;

Math. Comp. 86 (2017), 617-636

DOI: https://doi.org/10.1090/mcom/3151

Published electronically: May 3, 2016

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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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