Finite volume schemes for elliptic and elliptic-hyperbolic problems on triangular meshes

We present here a numerical comparison between different finite volume schemes for several equations. An elliptic equation of a diffusion-convection type and an elliptic-hyperbolic coupled system will be considered on an open bounded set Omega of R-2, using a triangular mesh for the discretization of Omega. A four point finite volume scheme (FV) and a 'weighted' finite Volume scheme (WFV) are presented along with the geometrical assumptions on the mesh. Both schemes are compared in the following cases: the pure diffusion operator, for which the WFV scheme may be seen as a finite element scheme with stabilization and numerical integration, and a diffusion-convection operator. a hyperbolic equation and a system of elliptic-hyperbolic equations. In all cases, the performance of both schemes are comparable, and the FV scheme is computationally cheaper.