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

Huangxin Chen, Shuyu Sun

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10 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)805-839
Number of pages35
JournalNumerische Mathematik
Volume136
Issue number3
DOIs
StatePublished - Dec 9 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): BAS/1/1351-01-01
Acknowledgements: 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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