502 IGPM502.pdf        March 2020
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