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

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    Type
    Article
    Authors
    Chen, Huangxin
    Sun, Shuyu cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    KAUST Grant Number
    BAS/1/1351-01-01
    Date
    2016-12-09
    Online Publication Date
    2016-12-09
    Print Publication Date
    2017-07
    Permanent link to this record
    http://hdl.handle.net/10754/622166
    
    Metadata
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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.
    Citation
    Chen H, Sun S (2016) A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media. Numerische Mathematik. Available: http://dx.doi.org/10.1007/s00211-016-0851-9.
    Sponsors
    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.
    Publisher
    Springer Nature
    Journal
    Numerische Mathematik
    DOI
    10.1007/s00211-016-0851-9
    Additional Links
    http://link.springer.com/article/10.1007%2Fs00211-016-0851-9
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00211-016-0851-9
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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