Error analysis of higher order trace finite element methods for the surface Stokes equations

Abstract: The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin-Helmholtz instability problem on the unit sphere.