6 problems

Let $V_h\subset[H^1(\Omega)]^3$ be constructed with continuous Lagrange elements of degree $k$. Let $\Sigma_h\subset H^1(\operatorname{curl},\Omega)$ be the space preceding $V_h$ i…

Let $V_h$ be constructed with continuous Lagrange elements of degree $k$, and choose $\Pi_h={{\nabla\cdot}\,}V_h$. The inf-sup condition is the existence of a constant $\beta>0$ su…

Let $u$ be the exact solution of the two-dimensional vector Laplacian problem and $u_h$ its approximation by the order-$k$ nonconforming primal hybrid finite element method. Let…

Let $\breve{\boldsymbol{U}}_{\tilde{\mathcal{T}}}^{\delta}$ be the discrete trial space on the refined partition…

Uniform condition-number conjecture. There exist $s<0$ and a constant $C$ such that

The refinement-process obstruction to property (PM). Under the stated approximation condition, no fixed pair $(\boldsymbol{a},\boldsymbol{b})$ can make property $(PM)$ hold through…