A posteriori error analysis of hybrid high-order method for the Stokes problem

TL;DR

This paper develops a residual-based a posteriori error estimator for the hybrid high-order method applied to the Stokes problem, enabling adaptive mesh refinement and verified through numerical experiments.

Contribution

It introduces a novel stabilizer for the HHO method and proves bounds for the error estimator, applicable in 2D and 3D on general meshes.

Findings

Error estimator bounds are established.

Adaptive algorithm improves solution accuracy.

Numerical tests confirm theoretical results.

Abstract

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, the 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.