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arXiv · 2508.10674

The Hu-Zhang element for linear elasticity on curved domains

Wei Chen·Xinyuan Du·Jun Hu
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Abstract

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.

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Wei Chen, Xinyuan Du, Jun Hu. 2025-08-14. The Hu-Zhang element for linear elasticity on curved domains. https://arxiv.org/abs/2508.10674

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