5 problems

Uniform inf-sup conjecture. Based on empirical investigations of the inf-sup constant $\gamma^\delta$ for the first-order ultra-weak formulation, it is conjectured that

Let $\Omega=[-1,1]^d$ with $d=2,3$, let $\mathcal{V}_h$ be the discrete velocity or pressure space as appropriate, and let $\Pi_h q_h$ be the projection used in the Rhie–Chow formu…

Crouzeix–Falk's conjecture. The pair

Let $\boldsymbol{V}_h\times Q_h$ be the Raviart–Thomas finite-element pair on the considered one-irregular quadrilateral meshes with hanging nodes, where … and … Here…

Let $\undertilde{G}{}^3_{h0}$ and $\mathbb{P}^2_{h0}$ denote the cubic nonconforming velocity space and the piecewise quadratic pressure space, respectively, on a triangulation of…