论文标题
无稳定后HHO后验错误控制
Stabilization-free HHO a posteriori error control
论文作者
论文摘要
杂交高阶方法（HHO）的已知后验误差分析将稳定贡献视为误差的一部分，也是误差估计器的一部分，用于有效且可靠的误差控制。本文规定了对简单网格的稳定贡献，并进行了无稳定误差分析，具有明确的基于残留的基于基于的后验误差估计器，用于自适应网格，以及基于平衡的确保上误差绑定（GUB）。泊松模型问题中的数值证据支持GUB导致分段能量规范中位移误差的现实上限。与显式基于残余的后验误差估计器相关的自适应网状算法恢复了计算基准中的最佳收敛速率。
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.
