7 problems

Consider the modulation approximation $\Psi$ for the dynamic Swift–Hohenberg equation. In the symmetric case $\mu(x)\equiv 0$, the error estimate remains exponentially small up to…

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 $E_{d,g}(x)$ be the error contribution defined by … where $S_{k,l}(x;d,g)$ is the sum defined in the source, and let $[d,g]$ be Artin admissible. Artin prime-pair error-term co…

Let $\Omega$ be the spatial domain, $h$ the mesh size, and $k$ the polynomial order in the CGDG discretization. Let $e_w$, $\bm{e}_\theta$, $\bm{E}_\kappa$, and $\bm{e}_\gamma$ den…

Isoparametric-element convergence conjecture. The use of general isoparametric elements should keep the quasi-optimal rate of convergence in non-energy norms.

Sharp half-order convergence conjecture. If $\omega\subsetneq\Omega$, the estimate is not sharp, and the order of convergence $1/2$ should hold as well.

Let $\bar{u}^{\rm atc}$ be the atomistic-to-continuum approximation, let $\bar{u}$ be the exact solution, let $\mathcal{L}$ be the computational lattice, let $\mathcal{L}_{\rm c}$…