The most traditional method for solving hyperbolic systems on unstructured grids  in multi dimensions is the finite volume (FV) method. The main building
blocks are conservative numerical fluxes and for higher order methods, MUSCL-type limiters. For scalar equations these scheme  are well examined and
convergence and error estimates have been proved. Higher order scheme work very well but the disadvantage of them is the large stencil, which is necessary
to achieve the higher order. Therefore schemes, like discontinuous Galerkin methods, with more compact stencils are very  important. Finite volume schemes
of first order are a special discontinuous Galerkin method. For higher order FV schemes they are different. Now the question has to be considered, which method
is more effective. We will present some numerical experiments concerning the comparison of both methods applied to  scalar equations and hyperbolic
systems.