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We explore the effects of mesh skewness on the accuracy of standard HybridHigh-Order (HHO) schemes for anisotropic diffusion equations. After defining anotion of regular skewed mesh sequences, which allows, e.g., for elements thatbecome more and more elongated during mesh refinement, we establish an errorestimate in which we precisely track the dependency of the local multiplicativeconstants in terms of the diffusion tensor and mesh skewness. This dependencymakes explicit an interplay between the local diffusion properties and thedistortion of the elements. We then provide several numerical results to assessthe practical convergence properties of HHO for highly anisotropic diffusion orhighly distorted meshes. These tests indicate a more robust behaviour than thetheoretical estimate indicates.

Interplay between diffusion anisotropy and mesh skewness in Hybrid High-Order schemes