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Stabilization of High Order Cut Finite Element Methods on Surfaces
(English)In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642Article in journal (Refereed) Accepted
Abstract [en]

We develop and analyze a stabilization term for cut finite elementapproximations of an elliptic second order partial differentialequation on a surface embedded in Rd. The new stabilization termcombines properly scaled normal derivatives at the surface togetherwith control of the jump in the normal derivatives across faces and provides control of the variation of the finite element solution on the active three dimensional elements that intersect the surface.We show that the condition number of the stiffness matrix is O(h^-2), where h is the mesh parameter. Thestabilization term works for linear as well as for higher-order elements and the derivation of its stabilizing properties is quite straightforward, which we illustrate by discussing the extension of the analysis to general n-dimensional smooth manifolds embedded in Rd, with codimension d-n.  We also state the properties of a general stabilization term that are sufficient to prove optimal scaling of the condition number and optimal error estimates in energy- and L2-norm.  We finally present numerical studies confirming our theoretical results.

Place, publisher, year, edition, pages
Oxford University Press.
Keywords [en]
CutFEM; high order discretization; PDEs on surfaces; properties of stabilization; condition number; error estimates.
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-249970OAI: oai:DiVA.org:kth-249970DiVA, id: diva2:1306643
Funder
Swedish Research Council, 2014-4804
Note

QCR 20190617

Available from: 2019-04-24 Created: 2019-04-24 Last updated: 2019-06-17Bibliographically approved

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Zahedi, Sara
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