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A cut finite element method for elliptic bulk problems with embedded surfaces
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2019 (English)In: GEM - International Journal on Geomathematics, ISSN 1869-2672, E-ISSN 1869-2680, Vol. 10, no 1, article id UNSP 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 Berlin/Heidelberg, 2019. Vol. 10, no 1, article id UNSP 10
Keywords [en]
Finite element, Unfitted, Embedded, Fractures
National Category
Computer Sciences Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-158762DOI: 10.1007/s13137-019-0120-zISI: 000463142200001PubMedID: 30873244OAI: oai:DiVA.org:umu-158762DiVA, id: diva2:1315213
Available from: 2019-05-13 Created: 2019-05-13 Last updated: 2019-05-13Bibliographically approved

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