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

Hybrid High-Order methods for elliptic diffusion problems have beenoriginally formulated for loads in the Lebesgue space $L^2(\Omega)$. In thispaper we devise and analyze a variant thereof, which is defined for any load inthe dual Sobolev space $H^{-1}(\Omega)$. The main feature of the presentvariant is that its $H^1$-norm error can be bounded only in terms of the$H^1$-norm best error in a space of broken polynomials. We establish thisestimate with the help of recent results on the quasi-optimality ofnonconforming methods. We prove also an improved error bound in the $L^2$-normby duality. Compared to previous works on quasi-optimal nonconforming methods,the main novelties are that Hybrid High-Order methods handle pairs of unknowns,and not a single function, and, more crucially, that these methods employ areconstruction that is one polynomial degree higher than the discrete unknowns.The proposed modification affects only the formulation of the discreteright-hand side. This is obtained by properly mapping discrete test functionsinto $H^1_0(\Omega)$.

A quasi-optimal variant of the Hybrid High-Order method for elliptic PDEs with $H^{-1}$ loads