Abstract
As in the previous chapters, we want to approximate the Poisson model problem, but this time we use the hybrid high-order (HHO) method. In this method, the discrete solution is composed of a pair: a face component that approximates the trace of the solution on the mesh faces and a cell component that approximates the solution in the mesh cells. The cell unknowns can be eliminated locally by static condensation. The two key ideas behind the HHO method are a local reconstruction operator and a local stabilization operator. Altogether the approximation setting is nonconforming since the solution is approximated by piecewise polynomials that can jump across the mesh interfaces. We also show that the HHO method is closely related to the hybridizable discontinuous Galerkin (HDG) method.
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