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A cut finite element method for elliptic bulk problems with embedded surfaces
Mathematics, University College London, London, United Kingdom.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0001-7352-1550
Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0002-2875-8433
2019 (English)In: GEM - International Journal on Geomathematics, ISSN 1869-2672, E-ISSN 1869-2680, Vol. 10, no 1, article id 10Article in journal (Refereed) Published
Abstract [en]

We propose an unfitted finite element method for flow in fractured porous media. The coupling across the fracture uses a Nitsche type mortaring, allowing for an accurate representation of the jump in the normal component of the gradient of the discrete solution across the fracture. The flow field in the fracture is modelled simultaneously, using the average of traces of the bulk variables on the fractures. In particular the Laplace–Beltrami operator for the transport in the fracture is included using the average of the projection on the tangential plane of the fracture of the trace of the bulk gradient. Optimal order error estimates are proven under suitable regularity assumptions on the domain geometry. The extension to the case of bifurcating fractures is discussed. Finally the theory is illustrated by a series of numerical examples. 

Place, publisher, year, edition, pages
Springer, 2019. Vol. 10, no 1, article id 10
Keywords [en]
Embedded, Finite element, Fractures, Unfitted, Fracture, Porous materials, Domain geometry, Embedded surfaces, Fractured porous media, Normal component, Optimal order error estimates, Regularity assumption, Finite element method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-43354DOI: 10.1007/s13137-019-0120-zISI: 000463142200001PubMedID: 30873244Scopus ID: 2-s2.0-85061086676Local ID: HOA JTH 2019;JTHMaterialISOAI: oai:DiVA.org:hj-43354DiVA, id: diva2:1297379
Available from: 2019-03-19 Created: 2019-03-19 Last updated: 2019-05-08Bibliographically approved

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Hansbo, PeterSamvin, David

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  • apa
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