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A new least squares stabilized Nitsche method for cut isogeometric analysis
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-1710-8494
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0001-5589-4521
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)ORCID iD: 0000-0001-7838-1307
2019 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 349, p. 1-16Article in journal (Refereed) Published
Abstract [en]

We derive a new stabilized symmetric Nitsche method for enforcement of Dirichlet boundary conditions for elliptic problems of second order in cut isogeometric analysis (CutIGA). We consider C1 splines and stabilize the standard Nitsche method by adding a certain elementwise least squares terms in the vicinity of the Dirichlet boundary and an additional term on the boundary which involves the tangential gradient. We show coercivity with respect to the energy norm for functions in H2(Ω) and optimal order a priori error estimates in the energy and L2 norms. To obtain a well posed linear system of equations we combine our formulation with basis function removal which essentially eliminates basis functions with sufficiently small intersection with Ω. The upshot of the formulation is that only elementwise stabilization is added in contrast to standard procedures based on ghost penalty and related techniques and that the stabilization is consistent. In our numerical experiments we see that the method works remarkably well in even extreme cut situations using a Nitsche parameter of moderate size.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 349, p. 1-16
Keywords [en]
Fictitious domain methods, Nitsche’s method, Least squares stabilization, Isogeometric analysis
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-156840DOI: 10.1016/j.cma.2019.02.011Scopus ID: 2-s2.0-85062154279OAI: oai:DiVA.org:umu-156840DiVA, id: diva2:1292662
Funder
Swedish Research Council, 2013-4708Swedish Research Council, 2017-03911Swedish Foundation for Strategic Research , AM13-0029eSSENCE - An eScience CollaborationAvailable from: 2019-03-01 Created: 2019-03-01 Last updated: 2019-06-13Bibliographically approved

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Elfverson, DanielLarson, Mats G.Larsson, Karl

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