The hybrid-high order (HHO) scheme has many successful applications including linear elasticity as the first step towards computational solid mechanics. The striking advantage is the simplicity among other higher-order nonconforming schemes and its geometric flexibility as a polytopal method on the expanse of a parameter-free refined stabilization. The classical suggestion of a locking-free HHO discretization requires a split of the the reconstruction terms with an additional reconstruction of the divergence operator that might be motivated by the Stokes equations for the robust approximation in the incompressible limit, when one Lam\'e parameter $\lambda\to\infty$ becomes very large. This paper utilizes just one reconstruction operator for the linear Green strain and therefore does not rely on a split in deviatoric and spherical behavior. The a priori error analysis provides quasi-best approximation with $\lambda$-independent equivalence constants. The reliable and (up to data oscillations) efficient a posteriori error estimates are stabilization-free and $\lambda$-robust. The error analysis is carried out on simplicial meshes to allow conforming piecewise polynomials finite elements in the kernel of the stabilization terms. Numerical benchmarks provide empirical evidence for optimal convergence rates of the a posteriori error estimator in some associated adaptive mesh-refining algorithm also in the incompressible limit.

翻译：混合高阶（HHO）格式已在多个领域取得成功应用，其中线性弹性问题作为计算固体力学的首个步骤具有重要意义。该方法的显著优势在于其相较于其他高阶非协调格式的简洁性，以及作为多面体方法在无参数精细化稳定代价下呈现的几何灵活性。经典的无锁HHO离散化方案要求对重构项进行分裂，并额外重构散度算子——这一设计可能受斯托克斯方程启发，旨在当拉梅参数$\lambda\to\infty$趋于无穷大时实现不可压缩极限下的鲁棒逼近。本文仅采用单一重构算子处理线性格林应变，因此无需依赖于偏斜-球状行为的分解。先验误差分析提供了与$\lambda$无关的等价常数下的拟最优逼近。可靠且（直至数据振荡）高效的后验误差估计无需稳定化处理且具有$\lambda$鲁棒性。误差分析在单纯形网格上进行，以允许在稳定项核空间中采用相容的分片多项式有限元。数值基准测试表明，所提出的后验误差估计器在相关自适应网格细化算法中（包括不可压缩极限情形下）具有最优收敛速率。