Stabilization-free HHO a posteriori error control

Abstract The known a posteriori error analysis of hybrid high-order methods treats the stabilization contribution as part and estimator for an efficient reliable control. This paper circumvents on simplicial meshes arrives at stabilization-free with explicit residual-based adaptive mesh-refining well equilibrium-based guaranteed upper bound (GUB). Numerical evidence in Poisson model problem supports that GUB leads to realistic bounds displacement piecewise energy norm. algorithm associated recovers optimal convergence rates computational benchmarks.