The Hu-Zhang element for linear elasticity on curved domains

Abstract: This paper extends the Hu-Zhang element for linear elasticity problems 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 result, which is overcome by establishing a novel inf-sup condition. Optimal convergence rates are achieved for all variables except the stress $L^2$-error. 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 rectified by local $p$-enrichment in the Hu-Zhang space on curved boundary elements. Some numerical experiments validate the theoretical results.