We present a residual-based a posteriori error estimator for the hybrid high-order (HHO) method for the Stokes model problem. Both the proposed HHO method and error estimator are valid in two and three dimensions and support arbitrary approximation orders on fairly general meshes. The upper bound and lower bound of the error estimator are proved, in which proof, a key ingredient is a novel stabilizer employed in the discrete scheme. By using the given estimator, adaptive algorithm of HHO method is designed to solve model problem. Finally, the expected theoretical results are numerically demonstrated on a variety of meshes for model problem.

翻译：我们提出了一个用于斯托克斯模型问题的混合高顺序(HHO)方法的后置误差测算仪。 拟议的HHO方法和误差测算仪在两个和三个方面都是有效的, 并且支持对相当普通的 meshes 的任意近似测算。 错误测算仪的上界和下界被证明, 其中证明, 关键成分是离散方案中使用的一个新稳定剂。 通过使用给定的测算仪, HHHO方法的适应性算法旨在解决模型问题。 最后, 预期的理论结果在模型问题的各种模类中以数字方式展示。