Abstract
In this work we investigate the conservativity of the cell centered Galerkin method of (Di Pietro, Cell centered Galerkin methods for diffusive problems, M2AN Math. Model. Numer. Anal., 46(1):111-144, 2012) and provide an analytical expression for the conservative flux. The relation with the SUSHI method of (Eymard, Gallouët, and Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes, SUSHI: a scheme using stabilization and hybrid interfaces, IMA J. Num. Anal., 30(4):1009-1043, 2010) and with discontinuous Galerkin methods is also explored. The theoretical results are assessed on a numerical example using standard as well as general polygonal grids.