Burman, E;
Hansbo, P;
Larson, MG;
Samvin, D;
(2019)
A cut finite element method for elliptic bulk problems with embedded surfaces.
GEM - International Journal on Geomathematics
, 10
, Article 10. 10.1007/s13137-019-0120-z.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | A cut finite element method for elliptic bulk problems with embedded surfaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s13137-019-0120-z |
| Publisher version: | https://doi.org/10.1007/s13137-019-0120-z |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | Finite element, Unfitted, Embedded, Fractures |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10068657 |
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