A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilizationReport as inadecuate




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* Corresponding author 1 EDF R&D - EDF Recherche et Développement 2 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 3 UCL London - Department of Mathematics

Abstract : We devise and analyze vertex-based schemes on polyhedral meshes to approximate advection-reaction equations. Error estimates of order 3-2 in the discrete inf-sup stability norm are established. The two key ingredients are a local poly-hedral reconstruction map leaving affine polynomials invariant, and a local design of stabilization whereby gradient jumps are only penalized across some subfaces in the interior of each mesh cell. Numerical results are presented on three-dimensional polyhedral meshes.

Keywords : Polyhedral meshes Advection-reaction problems Continuous interior penalty





Author: Pierre Cantin - Jérôme Bonelle - Erik Burman - Alexandre Ern -

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



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