An edge-based scheme on polyhedral meshes for vector advection-reaction equationsReport as inadecuate




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1 EDF R&D - EDF Recherche et Développement 2 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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.





Author: Pierre Cantin - Alexandre Ern -

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



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