ABSTRACT
Among the numerical methods used for the spatial resolution of partial differential equations (PDE), the finite differences method (FD) and the finite elements (FE) method use a local approximation for the functions; for instance, the FE are based on low-order polynomials, whose support-the subdomain over which the function is not zero-is very reduced with respect to the complete resolution domain. This allows to remove the strong coupling between the approximation functions over each finite element. The corresponding matrix systems are therefore more easily solved, their being very often block-diagonal and sparse. Finite volumes methods (FV) use the conservative formulation of the PDEs, and evaluate integrals over the elementary volumes, but eventually require FD approximations for the differential operators.
