A Multi-scale Hybrid High-Order methodReport as inadecuate

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1 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 2 EPFL - Ecole Polytechnique Fédérale de Lausanne

Abstract : We devise a multi-scale Hybrid High-Order HHO method. The method hinges on hybrid discrete unknowns that are polynomials attached to mesh elements and faces, and on a multi-scale reconstruction operator, that maps onto a fine-scale space spanned by oscillatory basis functions. The method handles arbitrary orders of approximation k >= 0, and is applicable on general meshes. For face-based unknowns that are polynomials of degree k, we devise two versions of the method, depending on the polynomial degree k - 1 or k of cell-based unknowns. We prove, in the case of periodic coefficients, an energy-error estimate of the form ε^1-2 + H^k+1 + ε^1-2H^-1-2.

Keywords : Polytopal discretization methods Arbitrary-order General meshes Multi-scale methods

Author: Matteo Cicuttin - Alexandre Ern - Simon Lemaire -

Source: https://hal.archives-ouvertes.fr/


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