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 generalise a hybridized discontinuous Galerkin method for incompressibleflow problems to non-affine cells, showing that with a suitable element mappingthe generalised method preserves a key invariance property that eludes mostmethods, namely that any irrotational component of the prescribed force isexactly balanced by the pressure gradient and does not affect the velocityfield. This invariance property can be preserved in the discrete problem if theincompressibility constraint is satisfied in a sufficiently strong sense. Wederive sufficient conditions to guarantee discretely divergence-free functionsare exactly divergence-free and give examples of divergence-free finiteelements on meshes with triangular, quadrilateral, tetrahedral, or hexahedralcells generated by a (possibly non-affine) map from their respective referencecells. In the case of quadrilateral cells, we prove an optimal error estimatefor the velocity field that does not depend on the pressure approximation. Ouranalysis is supported by numerical results.

computer methods in applied mechanics and engineering

Design and analysis of an exactly divergence-free hybridized  discontinuous Galerkin method for incompressible flows on meshes with  quadrilateral cells