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Stabilized CutFEM for the convection problem on surfaces
UCL, Department of Mathematics, London, United Kingdom.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0001-7352-1550
Umeå Universitet, Department of Mathematics and Mathematical Statistics, Umeå, Sweden.
The Royal Institute of Technology (KTH), Department of Mathematics, Stockholm, Sweden.
2019 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 141, no 1, p. 103-139Article in journal (Refereed) Published
Abstract [en]

We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a background mesh consisting of tetrahedra in an arbitrary way and the finite element space consists of piecewise linear continuous functions defined on the background mesh. The variational form involves integrals on the surface and the gradient jump stabilization term is defined on the full faces of the tetrahedra. The stabilization term serves two purposes: first the method is stabilized and secondly the resulting linear system of equations is algebraically stable. We establish stability results that are analogous to the standard meshed flat case and prove h3 / 2 order convergence in the natural norm associated with the method and that the full gradient enjoys h3 / 4 order of convergence in L2. We also show that the condition number of the stiffness matrix is bounded by h- 2. Finally, our results are verified by numerical examples. 

Place, publisher, year, edition, pages
Springer, 2019. Vol. 141, no 1, p. 103-139
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-41510DOI: 10.1007/s00211-018-0989-8ISI: 000457025700004Scopus ID: 2-s2.0-85052521788Local ID: HOA JTH 2019;JTHMaterialISOAI: oai:DiVA.org:hj-41510DiVA, id: diva2:1249600
Funder
Swedish Foundation for Strategic Research , AM13-0029Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708Swedish Research Council, 2014-4804eSSENCE - An eScience CollaborationAvailable from: 2018-09-19 Created: 2018-09-19 Last updated: 2019-02-20Bibliographically approved

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Hansbo, Peter

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