The known a posteriori error analysis of hybrid high-order methods (HHO) treats the stabilization contribution as part of the error and as part of the error estimator for an efficient and reliable error control. This paper circumvents the stabilization contribution on simplicial meshes and arrives at a stabilization-free error analysis with an explicit residual-based a posteriori error estimator for adaptive mesh-refining as well as an equilibrium-based guaranteed upper error bound (GUB). Numerical evidence in a Poisson model problem supports that the GUB leads to realistic upper bounds for the displacement error in the piecewise energy norm. The adaptive mesh-refining algorithm associated to the explicit residual-based a posteriori error estimator recovers the optimal convergence rates in computational benchmarks.

翻译：混合高阶方法（HHO）的已知后验误差分析将稳定化贡献视为误差和误差估计器的一部分，以实现高效可靠的误差控制。本文在单纯形网格上规避了稳定化贡献，并提出了一种无稳定化的误差分析方法，该方法包含用于自适应网格细化的显式残差型后验误差估计器，以及基于平衡的保证误差上界（GUB）。泊松模型问题的数值证据表明，GUB在分片能量范数下为位移误差提供了真实的上界。与显式残差型后验误差估计器相关的自适应网格细化算法在计算基准测试中恢复了最优收敛速率。