We establish the equivalence between Multiscale Hybrid-Mixed (MHM) and Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under idealized assumption that local problems defining multiscale basis functions are exactly solved, we prove holds general polytopal (coarse) meshes arbitrary approximation orders. also leverage interchange of propert...

We prove error estimates for the wave equation semi-discretized in space by hybrid high-order (HHO) method. These lead to optimal convergence rates smooth solutions. consider first second-order formulation time, which we establish $${\varvec{H}}^1$$ and $${\varvec{L}}^2$$ -error estimates, then first-order formulation, estimates. For both formulations, semi-discrete HHO scheme has close links w...