Inf-sup stability of geometrically unfitted Stokes finite elements
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- by Johnny Guzmán and Maxim Olshanskii PDF
- Math. Comp. 87 (2018), 2091-2112 Request permission
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.References
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Additional Information
- Johnny Guzmán
- Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
- MR Author ID: 775211
- Email: johnny_guzman@brown.edu
- Maxim Olshanskii
- Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
- MR Author ID: 343398
- Email: molshan@math.uh.edu
- 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. - © Copyright 2017 American Mathematical Society
- Journal: Math. Comp. 87 (2018), 2091-2112
- MSC (2010): Primary 65N30, 65N12, 76D07, 65N85
- DOI: https://doi.org/10.1090/mcom/3288
- MathSciNet review: 3802428