492 IGPM492.pdf        September 2019
TITLE Inf-sup stability of the trace P2-P1 Taylor-Hood 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 Taylor-Hood (continuous P2-P1) bulk elements is proposed. A so-called 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 inf-sup stability of the trace P2-P1 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
DOI 10.1090/mcom/3551
PUBLICATION Mathematics of Computation