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A stabilized cut streamline diffusion finite element method for convection-diffusion problems on surfaces
UCL, Dept Math, London WC1E 6BT, England..
Jonkoping Univ, Dept Mech Engn, SE-55111 Jonkoping, Sweden..
Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden..
Umea Univ, Dept Math & Math Stat, SE-90187 Umea, 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 UNSP 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 R-d. 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 SCIENCE SA , 2020. Vol. 358, article id UNSP 112645
Keywords [en]
Cut finite element method, Convection-diffusion-reaction, PDEs on surfaces, Streamline diffusion, Continuous interior penalty
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-265195DOI: 10.1016/j.cma.2019.112645ISI: 000496915700036Scopus ID: 2-s2.0-85072756632OAI: oai:DiVA.org:kth-265195DiVA, id: diva2:1380782
Note

QC 20191219

Available from: 2019-12-19 Created: 2019-12-19 Last updated: 2019-12-19Bibliographically approved

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Zahedi, Sara

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