Conditioning of a Hybrid High-Order Scheme on Meshes with Small Faces

Santiago Badia, Jérôme Droniou, Liam Yemm

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5 Citations (Scopus)


We conduct a condition number analysis of a Hybrid High-Order (HHO) scheme for the Poisson problem. We find the condition number of the statically condensed system to be independent of the number of faces in each element, or the relative size between an element and its faces. The dependence of the condition number on the polynomial degree is tracked. Next, we consider HHO schemes on cut background meshes, which are commonly used in unfitted discretisations. It is well known that the linear systems obtained on these meshes can be arbitrarily ill-conditioned due to the presence of sliver-cut and small-cut elements. We show that the condition number arising from HHO schemes on such meshes is not as negatively effected as those arising from conforming methods. We describe how the condition number can be improved by aggregating ill-conditioned elements with their neighbours.

Original languageEnglish
Article number71
Number of pages23
JournalJournal of Scientific Computing
Issue number2
Publication statusPublished - Aug 2022


  • Condition number
  • Hybrid High-Order methods
  • Small faces

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