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Mathematics of Computation

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Inf-sup stability of geometrically unfitted Stokes finite elements


Authors: Johnny Guzmán and Maxim Olshanskii
Journal: Math. Comp. 87 (2018), 2091-2112
MSC (2010): Primary 65N30, 65N12, 76D07, 65N85
DOI: https://doi.org/10.1090/mcom/3288
Published electronically: December 22, 2017
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Abstract: This paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a class of unfitted finite element methods for the Stokes and Stokes interface problems, such as Nitsche-XFEM or cutFEM. The error analysis is presented for the Stokes problem. All assumptions made in the paper are satisfied once the background mesh is shape-regular and fine enough.


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Additional Information

Johnny Guzmán
Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Email: johnny_guzman@brown.edu

Maxim Olshanskii
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: molshan@math.uh.edu

DOI: https://doi.org/10.1090/mcom/3288
Keywords: XFEM, cutFEM, Stokes problem, LBB condition, finite elements
Received by editor(s): May 31, 2016
Received by editor(s) in revised form: December 3, 2016, April 11, 2017, and April 18, 2017
Published electronically: December 22, 2017
Additional Notes: The first author was partially supported by NSF through the Division of Mathematical Sciences grant 1318108.
The second author was partially supported by NSF through the Division of Mathematical Sciences grants 1522252, 1717516.
Article copyright: © Copyright 2017 American Mathematical Society

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