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Cut finite elements for convection in fractured domains
University College London, UK, Department of Mathematics.ORCID iD: 0000-0003-4287-7241
Jönköping University, School of Engineering, JTH, Product Development.ORCID iD: 0000-0001-7352-1550
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0001-7838-1307
2019 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 179, p. 726-734Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 179, p. 726-734
Keywords [en]
Convection problems, Fractured domains, Mixed-dimensional domains, Galerkin least squares, A priori error estimates
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-158254DOI: 10.1016/j.compfluid.2018.07.022ISI: 000467514000053Scopus ID: 2-s2.0-85052134188OAI: oai:DiVA.org:umu-158254DiVA, id: diva2:1305552
Funder
Swedish Research Council, 2013-4708Swedish Research Council, 2017-03911Swedish Research Council, 2018-05262Swedish Foundation for Strategic Research , AM13-0029eSSENCE - An eScience Collaboration, -Available from: 2019-04-17 Created: 2019-04-17 Last updated: 2019-06-18Bibliographically approved

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Larson, Mats G.Larsson, Karl

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