8 problems

Let $u_{0}$ be the solution of the homogenized equation, and let $u_{\mathcal{D}^{\text{p}}}^{\epsilon}$ be the solution of the partially dilation-dilated equation. Motivated by th…

Actual decay-rate conjecture. The actual decay rate is

Optimal local convergence-rate conjecture. The optimal local convergence rate of MS-GFEM is

Let MSTLS denote the modified sequential thresholding least-squares algorithm, and distinguish its original formulation from the simplified hard-thresholding formulation analyzed i…

Vanishing-scale transfer-spectrum conjecture. For at least the considered test case, this independence result should transfer to

Let $\Omega$ be the computational domain, let $\Gamma$ be the interface between the fine finite-element region and the coarse oversampling MsFEM region, let $H$ be the coarse-mesh…

Let $varsigma_k$ be smooth boundary functions, for example traces of harmonic polynomials. Let $u_{varsigma_k}$ be the corresponding A-harmonic function and $u_{varsigma_k}^{h}$ it…

FLAVOR error-growth conjecture. The observed linear growth of the error with the total simulation time is a consequence of FLAVOR being symplectic, and this linear growth holds onl…