492

IGPM492.pdf September 2019 
TITLE 
Infsup stability of the trace P2P1 TaylorHood elements for surface PDEs 
AUTHORS 
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov 
ABSTRACT 
The paper studies a geometrically unfitted finite element method (FEM), known as
trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth
surface. A trace FEM based on standard TaylorHood (continuous P2P1) bulk elements is proposed.
A socalled volume normal derivative stabilization, known from the literature on trace FEM, is an
essential ingredient of this method. The key result proved in the paper is an infsup stability of
the trace P2P1 finite element pair, with the stability constant uniformly bounded with respect
to the discretization parameter and the position of the surface in the bulk mesh. Optimal order
convergence of a consistent variant of the finite element method follows from this new stability
result and interpolation properties of the trace FEM. Properties of the method are illustrated with
numerical examples. 
KEYWORDS 
surface Stokes problem, trace finite element method, Taylor–Hood elements, material surfaces, fluidic membranes 