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A stabilized cut streamline diffusion finite element method for convection–diffusion problems on surfaces
Department of Mathematics, University College London, 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, Umeå, Sweden.
Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden.
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2020 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 358, article id 112645Article in journal (Refereed) Published
Abstract [en]

We develop a stabilized cut finite element method for the stationary convection–diffusion problem on a surface embedded in Rd. The cut finite element method is based on using an embedding of the surface into a three dimensional mesh consisting of tetrahedra and then using the restriction of the standard piecewise linear continuous elements to a piecewise linear approximation of the surface. The stabilization consists of a standard streamline diffusion stabilization term on the discrete surface and a so called normal gradient stabilization term on the full tetrahedral elements in the active mesh. We prove optimal order a priori error estimates in the standard norm associated with the streamline diffusion method and bounds for the condition number of the resulting stiffness matrix. The condition number is of optimal order for a specific choice of method parameters. Numerical examples supporting our theoretical results are also included. 

Place, publisher, year, edition, pages
Elsevier, 2020. Vol. 358, article id 112645
Keywords [en]
Continuous interior penalty, Convection–diffusion–reaction, Cut finite element method, PDEs on surfaces, Streamline diffusion, Diffusion, Mesh generation, Number theory, Piecewise linear techniques, Stabilization, Stiffness matrix, Interior penalties, Piecewise linear approximations, Priori error estimate, Streamline diffusion methods, Streamline-diffusion finite element methods, Tetrahedral elements, Finite element method
National Category
Materials Engineering Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-46549DOI: 10.1016/j.cma.2019.112645Scopus ID: 2-s2.0-85072756632Local ID: ;JTHMaterialISOAI: oai:DiVA.org:hj-46549DiVA, id: diva2:1360713
Funder
Swedish Research Council, 2011-4992, 2013-4708Swedish Foundation for Strategic Research , AM13-0029,PHAvailable from: 2019-10-14 Created: 2019-10-14 Last updated: 2019-10-14Bibliographically approved

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Hansbo, Peter

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