Inf-sup stability of geometrically unfitted Stokes finite elements
Provides a theoretical foundation for unfitted finite element methods for Stokes problems, benefiting computational fluid dynamics with complex geometries.
The paper proves inf-sup stability for several Stokes finite elements on unfitted meshes, enabling optimal error estimates for unfitted methods like Nitsche-XFEM and cutFEM. The analysis covers 2D and 3D Stokes problems with smooth or polygonal domains.
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.