Inf-sup stability of the trace $\mathbf {P}_2$–$P_1$ Taylor–Hood elements for surface PDEs

The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of Stokes system posed on closed smooth surface. A based standard Taylor-Hood (continuous P2-P1) bulk elements is proposed. so-called volume normal derivative stabilization, from literature an essential ingredient this method. key result proved in inf-sup stability P2-P1 pair, with constant uniformly bounded respect to discretization parameter and position surface mesh. Optimal order convergence consistent variant follows new interpolation properties FEM. Properties are illustrated examples.