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

Huangxin Chen, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

2 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

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