Numerische Mathematik

, Volume 136, Issue 3, pp 805–839 | Cite as

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

  • Huangxin Chen
  • Shuyu SunEmail author


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.

Mathematics Subject Classification

65N12 65N15 65N30 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific ComputingXiamen UniversityXiamenChina
  2. 2.Computational Transport Phenomena Laboratory, Division of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwalKingdom of Saudi Arabia

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