Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Parker, Charles, Süli, Endre
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083510981
Cites:
Cited by:
Related to: