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