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arXiv · 2403.04499

Pressure-improved Scott-Vogelius type elements

Nis-Erik Bohne·Benedikt Gräßle·Stefan A. Sauter
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Abstract

The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximation. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain $critical$ $vertices$ in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate.

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Nis-Erik Bohne, Benedikt Gräßle, Stefan A. Sauter. 2024-03-07. Pressure-improved Scott-Vogelius type elements. https://arxiv.org/abs/2403.04499

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