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

We present and analyse in this paper a novel colocated Finite Volume scheme for the solution of the Stokes problem. It has been developed following two main ideas. On one hand, the dis- cretization of the pressure gradient term is built as the discrete transposed of the velocity divergence term, the latter being evaluated using a natural nite volume approximation; this leads to a non- standard interpolation formula for the expression of the pressure on the edges of the control volumes. On the other hand, the scheme is stabilized using a nite volume analogue to the Brezzi-Pitkaranta technique. We prove that, under usual regularity assumptions for the solution (each component of the velocity in H2() and pressure in H1()), the scheme is rst order convergent in the usual nite volume discrete H1 norm and the L2 norm for respectively the velocity and the pressure, provided, in particu- lar, that the approximation of the mass balance uxes is of second order. With the above-mentioned interpolation formulae, this latter condition is satised only for particular meshings: acute angles trian- gulations or rectangular structured discretizations in two dimensions, and rectangular parallelepipedic structured discretizations in three dimensions. Numerical experiments conrm this analysis and show, in addition, a second order convergence for the velocity in a discrete L2 norm.

On a stabilized colocated Finite Volume scheme for the Stokes problem