7 problems

Bounded regularity subdivision conjecture. There exist $M_\epsilon$ and $M_\epsilon'$ such that

Let a family of three-dimensional Worsey–Farin splits be obtained from a family of shape-regular simplicial meshes. Shape regularity conjecture. The resulting family of Worsey–Fari…

Garanzha's conjecture. The variational problem proposed by Garanzha allows one to construct the best deformations compared with state-of-the-art algorithms.

Let $T$ be a tetrahedron, with $R_T$ defined by … where $l_1\leq l_2\leq\cdots\leq h_T$ are the edge lengths, and let the projected circumradius be the parameter defined for tetrah…

Grading of BiSec-MT. There exists a mesh size function $h\in L^1(\Omega)$ with grading $\gamma_h=2$ such that the constants in the equidistribution estimate depend only on…

Let $\{\mathbb{T}_h\}$ be decompositions of a polyhedron into tetrahedra, let $\mathbb{T}_h$ be one such decomposition, and let $T_0\in\mathbb{T}_h$. Denote by $h_{T_0}$ the diamet…

Let $\mathcal{H}yb_1$ and $\mathcal{H}yb_{12}$ be the continuous finite element spaces defined on hybrid hexahedral-tetrahedral meshes. Assume standard mesh shape and function regu…