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

Handle URI:
http://hdl.handle.net/10754/622166
Title:
A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media
Authors:
Chen, Huangxin; Sun, Shuyu ( 0000-0002-3078-864X )
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.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division
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.
Publisher:
Springer Nature
Journal:
Numerische Mathematik
KAUST Grant Number:
BAS/1/1351-01-01
Issue Date:
9-Dec-2016
DOI:
10.1007/s00211-016-0851-9
Type:
Article
ISSN:
0029-599X; 0945-3245
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.
Additional Links:
http://link.springer.com/article/10.1007%2Fs00211-016-0851-9
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorChen, Huangxinen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2017-01-02T08:42:35Z-
dc.date.available2017-01-02T08:42:35Z-
dc.date.issued2016-12-09en
dc.identifier.citationChen 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.en
dc.identifier.issn0029-599Xen
dc.identifier.issn0945-3245en
dc.identifier.doi10.1007/s00211-016-0851-9en
dc.identifier.urihttp://hdl.handle.net/10754/622166-
dc.description.abstractIn 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.en
dc.description.sponsorshipHuangxin 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.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007%2Fs00211-016-0851-9en
dc.titleA residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous mediaen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalNumerische Mathematiken
dc.contributor.institutionSchool of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, Chinaen
kaust.authorChen, Huangxinen
kaust.authorSun, Shuyuen
kaust.grant.numberBAS/1/1351-01-01en
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