English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokesflows are considered. The focus lies on robust estimates for the kinetic anddissipation energies in a twofold sense. Firstly, pressure-robustness ensuresthe fulfilment of a fundamental invariance principle and velocity errorestimates are not corrupted by the pressure approximability. Secondly,$Re$-semi-robustness means that constants appearing on the right-hand side ofkinetic and dissipation energy error estimates (including Gronwall constants)do not explicitly depend on the Reynolds number. Such estimates rely on theessential regularity assumption $\nabla u \in L^1(0,T;L^\infty(\Omega))$ whichis discussed in detail. In the sense of best practice, we review and establishpressure- and $Re$-semi-robust estimates for pointwise divergence-free$H^1$-conforming FEM (like Scott-Vogelius pairs or certain isogeometric basedFEM) and pointwise divergence-free $H$(div)-conforming discontinuous GalerkinFEM. For convection-dominated problems, the latter naturally includes an upwindstabilisation for the velocity which is not gradient-based.

Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations