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A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media

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Abstract

In this paper we develop an a posteriori error estimator for a mixed finite element method for single-phase Darcy flow in a two-dimensional fractured porous media. The discrete fracture model is applied to model the fractures by one-dimensional fractures in a two-dimensional domain. We consider Raviart–Thomas mixed finite element method for the approximation of the coupled Darcy flows in the fractures and the surrounding porous media. We derive a robust residual-based a posteriori error estimator for the problem with non-intersecting fractures. The reliability and efficiency of the a posteriori error estimator are established for the error measured in an energy norm. Numerical results verifying the robustness of the proposed a posteriori error estimator are given. Moreover, our numerical results indicate that the a posteriori error estimator also works well for the problem with intersecting fractures.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable comments and suggestions that led to an improved presentation of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, Fujian, 361005, China

    Huangxin Chen

  2. Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Kingdom of Saudi Arabia

    Huangxin Chen & Shuyu Sun

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  1. Huangxin Chen
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  2. Shuyu Sun
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Correspondence to Shuyu Sun.

Additional information

Huangxin Chen would like to thank the support from the King Abdullah University of Science and Technology where this work was carried out during his visit, and he also thanks the supports from the NSF of China (Grant No. 11201394), the Fundamental Research Funds for the Central Universities (Grant No. 20720150005) and Program for Prominent Young Talents in Fujian Province University. The work of Shuyu Sun was supported by King Abdullah University of Science and Technology (KAUST) through the Grant BAS/1/1351-01-01.

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Chen, H., Sun, S. A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media. Numer. Math. 136, 805–839 (2017). https://doi.org/10.1007/s00211-016-0851-9

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  • DOI: https://doi.org/10.1007/s00211-016-0851-9

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