Robust Hybrid High-Order Method on Polytopal Meshes with Small Faces

Jérôme Droniou, Liam Yemm

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11 Citations (Scopus)

Abstract

We design a Hybrid High-Order (HHO) scheme for the Poisson problem that is fully robust on polytopal meshes in the presence of small edges/faces. We state general assumptions on the stabilisation terms involved in the scheme, under which optimal error estimates (in discrete and continuous energy norms, as well as L2L^{2}-norm) are established with multiplicative constants that do not depend on the maximum number of faces in each element, or the relative size between an element and its faces. We illustrate the error estimates through numerical simulations in 2D and 3D on meshes designed by agglomeration techniques (such meshes naturally have elements with a very large numbers of faces, and very small faces).

Original languageEnglish
Number of pages25
JournalComputational Methods in Applied Mathematics
Volume22
Issue number1
DOIs
Publication statusPublished - 22 Sept 2021

Keywords

  • Agglomerated Meshes
  • Error Analysis
  • Hybrid High-Order Scheme
  • Small Faces

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