Stabilization-free HHO a posteriori error control (Q6135912)

In this paper an extension of a posteriori error estimator for hybrid high-order methods is presented. In particular, this paper shows that the stabilization contribution on simplicial meshes can be circumvented. Here, a stabilization-free error analysis is performed and an explicit residual-based a posteriori error estimator is derived applicable both for adaptive mesh-refining as well as for an equilibrium-based guaranteed upper error bound. Numerical experiments are performed supporting the theoretical findings. Numerical results are presented for a Poisson model problem to support that the error estimator is the guaranteed error bound. The adaptive mesh-refining algorithm is applied based on the explicit residual-based a posteriori error estimator and the optimal convergence rates are obtained in several computational benchmarks.