Stabilization-free HHO a posteriori error control

TL;DR

This paper introduces a stabilization-free a posteriori error analysis for hybrid high-order methods, providing explicit residual-based error estimators and guaranteed upper bounds, improving efficiency and reliability in adaptive mesh refinement.

Contribution

It develops a novel stabilization-free error analysis for HHO methods with explicit estimators and guaranteed bounds, enhancing adaptive refinement accuracy.

Findings

GUB provides realistic upper bounds for displacement error

Adaptive algorithm achieves optimal convergence rates

Numerical results validate the effectiveness of the error estimators

Abstract

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.