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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper considers the discretization of the Stokes equations withScott--Vogelius pairs of finite element spaces on arbitrary shape-regularsimplicial grids. A novel way of stabilizing these pairs with respect to thediscrete inf-sup condition is proposed and analyzed. The key idea consists inenriching the continuous polynomials of order $k$ of the Scott--Vogeliusvelocity space with appropriately chosen and explicitly given Raviart--Thomasbubbles. This approach is inspired by [Li/Rui, IMA J. Numer. Anal, 2021], wherethe case $k=1$ was studied. The proposed method is pressure-robust, withoptimally converging $\boldsymbol{H}^1$-conforming velocity and a small$\boldsymbol{H}(\mathrm{div})$-conforming correction rendering the fullvelocity divergence-free. For $k\ge d$, with $d$ being the dimension, themethod is parameter-free. Furthermore, it is shown that the additional degreesof freedom for the Raviart--Thomas enrichment and also all non-constantpressure degrees of freedom can be condensated, effectively leading to apressure-robust, inf-sup stable, optimally convergent $\boldsymbol{P}_k \timesP_0$ scheme. Aspects of the implementation are discussed and numerical studiesconfirm the analytic results.

Inf-sup stabilized Scott--Vogelius pairs on general simplicial grids by Raviart--Thomas enrichment