Towards stabilization-free Hybrid High-Order methods for elliptic problems
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Hybrid High-Order (HHO) methods were introduced a decade ago as a new method in the class of Discontinuous Skeletal discretizations. The main features of HHO are the approximation of the solution with arbitrary order polynomials, support for fully polytopal meshes and easy hp-refinement. In recent years, the study of Galerkin methods suitable for polytopal meshes that avoid the use of a non-physical stabilization term has attracted the interest of the scientific community. We introduce and study numerically a variant of HHO for elliptic problems, posed on 2D and 3D polytopal domains and free of an explicit stabilization term.