Stability of high-order Scott-Vogelius elements for 2D non-Newtonian incompressible flow

We consider the stability of high-order Scott-Vogelius elements for 2D non-Newtonian incompressible flow problems. For elements of degree 4 or higher, we construct a right-inverse of the divergence operator that is stable uniformly in the polynomial degree N N from L p Lᵖ to W 1 , p W1,p , show that the associated inf-sup constant is bounded below by a constant that decays at worst like N − 3 | 1 2 − 1 p | N-3 | 1/2 - 1/p | , and construct local Fortin operators with stability constants explicit in the polynomial degree. We demonstrate these results with several numerical examples suggesting that the p p -version method can offer superior convergence rates over the h h -version method even in the non-Newtonian setting.