Towards stabilization-free Hybrid High-Order methods for elliptic problems

We devise and study Hybrid High-Order (HHO) methods in a stabilization-free formulation, i.e. based on discrete bilinear forms not requiring an additional, explicit stabilization term. The discretization hinges on newly defined reconstruction operators mapping on polynomial spaces richer than the ones used in standard HHO literature. Optimal order a priori error estimates are obtained with the expected HHO convergence rates. The well-posedness of the discrete scheme is currently only conjectured. Extensive numerical tests are presented, supporting the stability and robustness of the new methods and shedding a light on future theoretical developments.