English

Inf-sup stability of geometrically unfitted Stokes finite elements

Numerical Analysis 2017-04-24 v3

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.

Keywords

Cite

@article{arxiv.1605.09681,
  title  = {Inf-sup stability of geometrically unfitted Stokes finite elements},
  author = {Johnny Guzmán and Maxim Olshanskii},
  journal= {arXiv preprint arXiv:1605.09681},
  year   = {2017}
}