Stabilization-free HHO a posteriori error control

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. Keywords hybrid high-order • a posteriori • guaranteed upper error bounds • adaptive mesh refinement • equilibration • stabilization-free • computational comparisons This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) in the Priority Program 1748 Reliable simulation techniques in solid mechanics. Development of nonstandard discretization methods, mechanical and mathematical analysis under the projects BE 6511/1-1 and CA 151/22-2 as well as the European Union's Horizon 2020 research and innovation programme (Grant agreement No. 891734). The third author is also supported by the Berlin Mathematical School.