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

2025/09/23 by Parker, Charles, Süli, Endre · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2509.19488

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 \boldsymbolW^1,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)|}, 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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• A local Fortin projection for the Scott-Vogelius elements on general meshes
• Scott-Vogelius element and iterated penalty method for inhomogeneous Dirichlet boundary conditions

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