A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization

Pierre Cantin (1, 2) , Jérôme Bonelle (1) , Erik Burman (3) , Alexandre Ern (2)

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

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.

Mots clés: Polyhedral meshes; Advection-reaction problems; Continuous interior penalty

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Analyse fonctionnelle [math.FA]

Pierre Cantin, Jérôme Bonelle, Erik Burman, Alexandre Ern. A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization. Computers & Mathematics with Applications, 2016, ⟨10.1016/j.camwa.2016.07.038⟩. ⟨hal-01285957v2⟩