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Cut finite elements for convection in fractured domains
Department of Mathematics, University College London, United Kingdom.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0001-7352-1550
Department of Mathematics and Mathematical Statistics, Umeå University, Sweden.
Department of Mathematics and Mathematical Statistics, Umeå University, Sweden.
2019 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 179, p. 728-736Article 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. 728-736
Keywords [en]
A priori error estimates, Convection problems, Fractured domains, Galerkin least squares, Mixed-dimensional domains, Fracture, Mesh generation, Piecewise linear techniques, Porous materials, Convection problem, Coupling condition, Directional derivative, Divergence operators, Modeling porous medias, Piecewise linear, Priori error estimate, Finite element method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-41509DOI: 10.1016/j.compfluid.2018.07.022ISI: 000467514000053Scopus ID: 2-s2.0-85052134188Local ID: JTHMaterialISOAI: oai:DiVA.org:hj-41509DiVA, id: diva2:1249566
Available from: 2018-09-19 Created: 2018-09-19 Last updated: 2019-06-04Bibliographically approved

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Hansbo, Peter

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CiteExportLink to record
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  • apa
  • harvard1
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  • de-DE
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