In this work, we introduce and analyze a hp-Hybrid High-Order 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 formulate hp-convergence estimates for both the energy- and L2-norms of the error, which are the first results of this kind for Hybrid High-Order methods. The estimates are fully robust with respect to the heterogeneity of the diffusion coefficient, and show only a mild dependence on its (local) anisotropy. The ex- pected exponential convergence behaviour is numerically shown on a variety of meshes for both isotropic and strongly anisotropic diffusion problems.
An hp-Hybrid High-Order method for variable diffusion on general meshes / Aghili J; Di Pietro D; Ruffini B. - In: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS. - ISSN 1609-4840. - STAMPA. - 17:3(2017), pp. 359-376. [10.1515/cmam-2017-0009]
An hp-Hybrid High-Order method for variable diffusion on general meshes
Ruffini B
2017
Abstract
In this work, we introduce and analyze a hp-Hybrid High-Order 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 formulate hp-convergence estimates for both the energy- and L2-norms of the error, which are the first results of this kind for Hybrid High-Order methods. The estimates are fully robust with respect to the heterogeneity of the diffusion coefficient, and show only a mild dependence on its (local) anisotropy. The ex- pected exponential convergence behaviour is numerically shown on a variety of meshes for both isotropic and strongly anisotropic diffusion problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.