The known a posteriori error analysis of hybrid high-order methods 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.

已知的混合高阶方法的后验误差分析将稳定性贡献视为误差的一部分以及误差估计器的一部分，以实现高效且可靠的误差控制。本文规避了单纯网格上的稳定性贡献，并通过用于自适应网格细化的显式基于残差的后验误差估计器以及基于平衡的保证误差上限（GUB）来实现无稳定性误差分析。泊松模型问题中的数值证据支持 GUB 导致分段能量范数中位移误差的实际上限。与基于显式残差的后验误差估计器相关的自适应网格细化算法恢复了计算基准中的最佳收敛率。