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arXiv · 2509.19488

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

Charles Parker·Endre Süli
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Abstract

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 $\boldsymbol{W}^{1,p}$, show that the associated inf-sup constant is bounded below by a constant that decays at worst like $N^{-3\left| \frac{1}{2} - \frac{1}{p}\right|}$, 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 can offer superior convergence rates over the $h$-version method even in the non-Newtonian setting.

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Charles Parker, Endre Süli. 2025-09-23. Stability of high-order Scott-Vogelius elements for 2D non-Newtonian incompressible flow. https://arxiv.org/abs/2509.19488

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