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

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 c...

Full description

Saved in:
Bibliographic Details
Published in:Journal of scientific computing 2022-08, Vol.92 (2), p.71, Article 71
Main Authors: Badia, Santiago, Droniou, Jérôme, Yemm, Liam
Format: Article
Language:English
Subjects:
Algorithms
Boundary conditions
Computational Mathematics and Numerical Analysis
Conditioning
Estimates
Finite element analysis
Linear systems
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Partial differential equations
Polynomials
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-022-01913-9