502	RWTH Publication No: 824027        2020        IGPM502.pdf
TITLE	Error analysis of higher order trace finite element methods for the surface stokes equation
AUTHORS	Thomas Jankuhn, Maxim A. Olshanskii , Arnold Reusken, Alexander Zhiliakov
ABSTRACT	The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in R3. The method employs parametric Pk-Pk−1 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.
KEYWORDS	surface Stokes equation, trace finite element method, Taylor-Hood finite elements
DOI	10.1515/jnma-2020-0017
PUBLICATION	Journal of Numerical Mathematics October 2020