Inserted: 4 jun 2020
Last Updated: 10 jun 2020
Journal: Comput. Methods Appl. Math.
In this work, we introduce and analyze an hp-hybrid high-order (hp-HHO) method for a variable diffusion problem. The proposed method is valid in arbitrary space dimension and for fairly general polytopal meshes. Variable approximation degrees are also supported. We prove hp-convergence estimates for both the energy-and L 2-norms of the error, which are the first of this kind for Hybrid High-Order methods. These results hinge on a novel hp-approximation lemma valid for general polytopal elements in arbitrary space dimension. The estimates are additionally fully robust with respect to the heterogeneity of the diffusion coefficient, and show only a mild dependence on the square root of the local anisotropy, improving previous results for HHO methods. The expected exponential convergence behavior is numerically demonstrated on a variety of meshes for both isotropic and strongly anisotropic diffusion problems.