Inf-sup stability of geometrically unfitted Stokes finite elements | Zendy

Johnny Guzmán | Zendy; Maxim A. Olshanskii | Zendy

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Inf-sup stability of geometrically unfitted Stokes finite elements

Author(s) -

Johnny Guzmán,

Maxim A. Olshanskii

Publication year - 2017

Publication title -

mathematics of computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.95

H-Index - 103

eISSN - 1088-6842

pISSN - 0025-5718

DOI - 10.1090/mcom/3288

Subject(s) - stokes problem , mathematics , finite element method , stability (learning theory) , stokes flow , property (philosophy) , domain (mathematical analysis) , extended finite element method , mathematical analysis , geometry , computer science , physics , philosophy , flow (mathematics) , epistemology , machine learning , thermodynamics

The 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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