The Hu-Zhang element for linear elasticity on curved domains

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Chen, Wei, Du, Xinyuan, Hu, Jun
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916922640039936
author Chen, Wei
Du, Xinyuan
Hu, Jun
author_facet Chen, Wei
Du, Xinyuan
Hu, Jun
contents This paper extends the Hu-Zhang element for linear elasticity to curved domains, preserving strong symmetry and H(div)-conformity. The non-polynomial structure of the curved Hu-Zhang element makes it difficult to analyze the stability, which is overcome by establishing a novel inf-sup condition. Optimal convergence rates are achieved for all variables except for the stress in the $L^2$-norm. This suboptimality originates from the fact that the divergence space of the curved Hu-Zhang element is not contained in the discrete displacement space, which is improved by local $p$-enrichment on boundary elements. Two numerical experiments validate the theoretical results.
format Preprint
id arxiv_https___arxiv_org_abs_2508_10674
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Hu-Zhang element for linear elasticity on curved domains
Chen, Wei
Du, Xinyuan
Hu, Jun
Numerical Analysis
65N12, 65N30, 74S05
This paper extends the Hu-Zhang element for linear elasticity to curved domains, preserving strong symmetry and H(div)-conformity. The non-polynomial structure of the curved Hu-Zhang element makes it difficult to analyze the stability, which is overcome by establishing a novel inf-sup condition. Optimal convergence rates are achieved for all variables except for the stress in the $L^2$-norm. This suboptimality originates from the fact that the divergence space of the curved Hu-Zhang element is not contained in the discrete displacement space, which is improved by local $p$-enrichment on boundary elements. Two numerical experiments validate the theoretical results.
title The Hu-Zhang element for linear elasticity on curved domains
topic Numerical Analysis
65N12, 65N30, 74S05
url https://arxiv.org/abs/2508.10674