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-co nvection type and an elliptic-hyperbolic coupled system will be consid ered 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) an d 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 schem e may be seen as a finite element scheme with stabilization and numeri cal integration, and a diffusion-convection operator. a hyperbolic equ ation and a system of elliptic-hyperbolic equations. In all cases, the performance of both schemes are comparable, and the FV scheme is comp utationally cheaper.