Type: Article
Publication Date: 2017-01-09
Citations: 3
DOI: https://doi.org/10.5539/jmr.v9n1p68
We introduced in (Fortin & Serghini Mounim, 2005) a new method which allows us to extend the connection between the finite volume and dual mixed hybrid (DMH) methods to advection-diffusion problems in the one-dimensional case. In the present work we propose to extend the results of (Fortin & Serghini Mounim, 2005) to multidimensional hyperbolic and parabolic problems. The numerical approximation is achieved using the Raviart-Thomas (Raviart & Thomas, 1977) finite elements of lowest degree on triangular or rectangular partitions. We show the link with numerous finite volume schemes by use of appropriate numerical integrations. This will permit a better understanding of these finite volume schemes and the large number of DMH results available could carry out their analysis in a unified fashion. Furthermore, a stabilized method is proposed. We end with some discussion on possible extensions of our schemes.