  We explore the effects of mesh skewness on the accuracy of standard Hybrid
High-Order (HHO) schemes for anisotropic diffusion equations. After defining a
notion of regular skewed mesh sequences, which allows, e.g., for elements that
become more and more elongated during mesh refinement, we establish an error
estimate in which we precisely track the dependency of the local multiplicative
constants in terms of the diffusion tensor and mesh skewness. This dependency
makes explicit an interplay between the local diffusion properties and the
distortion of the elements. We then provide several numerical results to assess
the practical convergence properties of HHO for highly anisotropic diffusion or
highly distorted meshes. These tests indicate a more robust behaviour than the
theoretical estimate indicates.
