# The Scott-Vogelius finite elements revisited

## TL;DR

This paper proves the inf-sup stability of Scott-Vogelius finite elements for higher polynomial degrees on shape-regular meshes, enhancing their theoretical foundation for fluid dynamics simulations.

## Contribution

It establishes the stability of Scott-Vogelius elements for quartic and higher degree velocity fields on shape-regular meshes, which was previously unproven.

## Key findings

- Proves inf-sup stability for k ≥ 4
- Applicable to shape-regular meshes
- Extends theoretical understanding of finite element stability

## Abstract

We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher ($k \ge 4$).