Error estimate for a 1D-2D finite volume scheme. Comparison with a standard scheme on a 2D non-admissible mesh.

Marie-Claude Viallon (1)

1 MMCS - Modélisation mathématique, calcul scientifique

We study an hybrid finite volume scheme to solve a problem set in a domain consisting of several zones of different dimensions in space. For a linear 1D-2D model problem, we define a specific $H^1$ discrete norm and we state an error estimate in this norm. We compare the hybrid scheme to a classical scheme used on a 2D non-admissible mesh.

Mots clés: finite volume scheme; elliptic problem; error estimate; multi-scale domain

Domaines: Equations aux dérivées partielles [math.AP]

Marie-Claude Viallon. Error estimate for a 1D-2D finite volume scheme. Comparison with a standard scheme on a 2D non-admissible mesh.. Comptes rendus hebdomadaires des séances de l'Académie des sciences, 2013, 351, pp.47-51. ⟨10.1016/j.crma.2013.01.011⟩. ⟨hal-00916774⟩