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

Journal article

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 $N$ from $L^{p}$ to $W^{1,p}$, show that the associated inf-sup constant is bounded below by a constant that decays at worst like $N^{- \frac{1}{2} - \frac{1}{p}}$, and construct local Fortin operators with stability constants explicit in the polynomial degree. We demonstrate these results with several numerical examples suggesting that the $p$-version method offers superior convergence rates over the $h$-version method even in the non-Newtonian case.

Authors: Parker, C; Suli, E

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: American Mathematical Society
• Journal: Mathematics of Computation
• Publication date: 2025-09-01
• Acceptance date: 2026-03-09
• EISSN: 1088-6842
• ISSN: 0025-5718
• Language: English