Numerical investigation of effectivity indices of space-time error indicators for Navier–Stokes equations

Order preserving SUPG stabilization for the virtual element formulation of advection–diffusion problems

“…We first prove (28) considering E ∈ T h . Regarding the terms involving the VEM stabilization, we first point out that, as a consequence of (17), we have…”

“…Going back to (39), we estimate the continuity of B supg,h , given by (23), (25) and (28), and the estimate on the VEM interpolator in (37):…”

“…Another issue related to advection-diffusion problems is the derivation of robust a posteriori error estimates. In such context, the term robustness refers to the property of obtaining a relation between the error and the error estimator with constants which are independent of the Péclet number [23][24][25][26][27][28]. An a posteriori analysis for the reactionconvection-diffusion problem with the VEM is provided in [29], not addressing robustness aspects and the SUPG-like stabilization issues.…”

Variational multiscale a posteriori error estimation for systems: The Euler and Navier–Stokes equations

“…Other explicit methods can be considered error indicators, like [33], where the curvature or second derivative of the solution is used to adapt the mesh size of compressible flow calculations. In this line, for the incompressible Navier-Stokes equation it can be mentioned the error indicator [34]. An example for anisotropy mesh adaptation for the shallow water equations can be found in [35].…”