Inf-sup stability of geometrically unfitted Stokes finite elements

Guzmán, Johnny; Olshanskii, Maxim

doi:10.1090/mcom/3288

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.

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