5 problems

Let $\{\mathcal{M}^{\ell}\}_{\ell=0}^{\ell_{\max}}$ be the sequence of consecutively globally refined unstructured quad meshes described above, and let $\mathcal{B}^{\ell}$ be the…

Localization conjecture. The number of Newton iterations required for the system to converge to a desired tolerance is dominated by a narrow region in space and time where the nonl…

Let a grid be sufficiently regular, and suppose that the cells near the boundary are aligned with the boundary itself, meaning that their faces are either orthogonal or parallel to…

Cost-increment conjecture. The cost increment factor for regular triangulation refinement is conjectured to satisfy

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…