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

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

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