Burman, E;
Hansbo, P;
Larson, MG;
Larsson, K;
(2019)
Cut finite elements for convection in fractured domains.
Computers & Fluids
, 179
pp. 726-734.
10.1016/j.compfluid.2018.07.022.
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Abstract
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain, which is a union of manifolds of different dimensions such that a d dimensional component always resides on the boundary of a d+1 dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem is formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is posed on a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.
| Type: | Article |
|---|---|
| Title: | Cut finite elements for convection in fractured domains |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.compfluid.2018.07.022 |
| Publisher version: | https://doi.org/10.1016/j.compfluid.2018.07.022 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Convection problems, Fractured domains, Mixed-dimensional domains, Galerkin least squares, A priori error estimates |
| UCL classification: | UCL 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/10058164 |
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