Inf-sup stability of geometrically unfitted Stokes finite elements

2016/05/31 by Guzmán, Johnny, Olshanskii, Maxim · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1605.09681

Abstract

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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