9 problems

Let $u$ be the exact solution and $u_h$ the numerical solution produced by the conservative flux optimization finite element scheme, with $\beta$, $\tau_D$, and $\boldsymbol{n}_e$…

Estimator-behaviour conjecture. The estimator behaviour reported in Tables 7 and 8 of Gorynina, Lozinski, and Picasso is due to the different a posteriori error estimator used ther…

Let $c_{\rm eff}$ be the local efficiency constant in the estimate … where $\eta_\nu$ is the vertex error estimator and $\mathcal E(\omega^\nu)$ is the corresponding local error me…

p-independence conjecture. For general meshes, the dependence of $C_{{\rm stab},\nu}$ on $p$ is artificial and can be removed, so that the stability estimates hold with a constant…

Interface-residual conjecture. The quantity $\eta^\Gamma$ can indicate the modelling error caused by replacing the 2D model by the 0D one, and can therefore drive the choice of the…

Suppose a snapshot matrix is compressed by a singular value decomposition, particularly when no error estimator is available or evaluating one is very costly. Adaptive-enrichment c…

Let $e_h=u-u_h$, let $K$ be an element of the mesh, and let $\tilde{\eta}_K$ denote the locally scaled residual estimator. Assume the superconvergence properties of…

Let an a posteriori error estimator for a finite element approximation to an $\bm{H}(\operatorname{curl})$ problem be appropriately constructed. Divergence-term conjecture. The est…

Dauge's conjecture. It is conjectured that