ON COMBINING FINITE ELEMENT METHODS AND FINITE VOLUME METHODS IN COMPUTATIONAL FLUID DYNAMICS

Finite volume schemes are widely used in the numerical solution of conservation laws such as those occuring in C.F.D. Finite element approximations are naturally well suited to second-order operators like those modelling diffusion terms. Then an attractive approach for solving time-dependent convection-dominated diffusion problems consists in combining finite volume for convection and finite element for diffusion. In this paper, we propose to provide a review and a numerical comparison of these approaches in the framework of triangular meshes in two-dimension. New methods for combining finite volumes and finite elements are also defined.