An edge-based scheme on polyhedral meshes for vector advection-reaction equations

Abstract : We devise and analyze an edge-based scheme on polyhedral meshes to approximate a vector advection-reaction problem. The well-posedness of the discrete problem is analyzed first under the classical positivity hypothesis of Friedrichs' systems that requires a lower bound on the lowest eigen-value of some tensor depending on the model parameters. We also prove stability when the lowest eigenvalue is null or even slightly negative if the mesh size is small enough. A priori error estimates are established for smooth solutions. Numerical results are presented on three-dimensional polyhedral meshes.
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Submitted on : Thursday, November 23, 2017 - 7:06:32 PM
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Pierre Cantin, Alexandre Ern. An edge-based scheme on polyhedral meshes for vector advection-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2017, ⟨10.1051/m2an/2016075⟩. ⟨hal-01324545v3⟩

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