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. This paper utilizes just one reconstruction operator for the linear Green strain and therefore does not rely on a split in deviatoric and spherical behaviour as in the classical HHO discretization. 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, where this paper provides corresponding assertions for the Stokes problem.

翻译：混合高阶（HHO）格式已在包括线性弹性在内的诸多领域得到成功应用，这是其迈向计算固体力学的第一步。其显著优势在于：相较于其他高阶非协调格式更为简洁，且作为一种多胞体方法具有几何灵活性，代价在于需要一种无参数的精化稳定化策略。本文仅采用单一重构算子处理线性格林应变，因此无需依赖经典HHO离散化中偏量与球量行为的分离。先验误差分析提供了具有$\lambda$无关等价常数的拟最佳逼近。可靠且（除数据振荡外）高效的后验误差估计无需稳定化项且具有$\lambda$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使用协调的分片多项式有限元。数值基准测试为后验误差估计器在相关自适应网格细化算法中的最优收敛速率提供了经验证据，该方法在不可压缩极限情形下依然有效——本文同时为斯托克斯问题给出了相应结论。