Pressure-improved Scott-Vogelius type elements
<|reference_start|>Pressure-improved Scott-Vogelius type elements: 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.<|reference_end|>
@article{bohne2024pressure-improved,
    title={Pressure-improved Scott-Vogelius type elements},
    author={Nis-Erik Bohne, Benedikt Gr"a{ss}le, Stefan A. Sauter},
    journal={arXiv preprint arXiv:2403.04499},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.04499},
    primaryClass={math.NA cs.NA}
}