Stability of high-order Scott-Vogelius elements for 2D non-Newtonian incompressible flow
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909803839750144 |
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| author | Parker, Charles Süli, Endre |
| author_facet | Parker, Charles Süli, Endre |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_19488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of high-order Scott-Vogelius elements for 2D non-Newtonian incompressible flow Parker, Charles Süli, Endre Numerical Analysis 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. |
| title | Stability of high-order Scott-Vogelius elements for 2D non-Newtonian incompressible flow |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.19488 |