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A cut finite element method for a model of pressure in fractured media

Burman, E; Hansbo, P; Larson, MG; (2020) A cut finite element method for a model of pressure in fractured media. Numerische Mathematik 10.1007/s00211-020-01157-5. (In press). Green open access

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Abstract

We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion. Starting from a common background bulk mesh, that covers the domain, finite element spaces are constructed for the interface and bulk subdomains leading to efficient computations of the coupling terms. The crack pressure field also uses the bulk mesh for its representation. The interface conditions are a generalized form of conditions of Robin type previously considered in the literature which allows the modeling of a range of flow regimes across the fracture. The method is robust in the following way: (1) Stability of the formulation in the full range of parameter choices; and (2) Not sensitive to the location of the interface in the background mesh. We derive an optimal order a priori error estimate and present illustrating numerical examples.

Type: Article
Title: A cut finite element method for a model of pressure in fractured media
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00211-020-01157-5
Publisher version: https://doi.org/10.1007/s00211-020-01157-5
Language: English
Additional information: © 2020 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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/10114356
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