In this paper, we clarify reconstruction-based discretization schemes for unstructured grids and discuss their economically high-order versions, which can achieve accuracy under certain conditions at little extra cost. The clarification leads to one of the most economical approaches: flux-and-solution-reconstruction (FSR) approach, where highly be constructed based on an extended kappa-scheme c...

We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of biharmonic problem. The support polyhedral meshes, rely on primal formulation problem, deliver $O(h^{k+1})$ $H^2$-error estimates when using polynomials order $k\ge0$ to approximate normal derivative mesh (inter)faces. Both HHO hinge a stabilization in spirit Lehrenfeld Schöberl second-order PDEs. cell ...