Journal
COMPUTERS & FLUIDS
Volume 179, Issue -, Pages 728-736Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compfluid.2018.07.022
Keywords
Convection problems; Fractured domains; Mixed-dimensional domains; Galerkin least squares; A priori error estimates
Funding
- Swedish Foundation for Strategic Research Grant [AM13-0029]
- Swedish Research Council [2013-4708, 2017-03911]
- Swedish Research Programme Essence
- EPSRC [EP/P01576X/1, EP/P012434/1]
- EPSRC [EP/P01576X/1] Funding Source: UKRI
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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. (C) 2018 Elsevier Ltd. All rights reserved.
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