The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convec...

Stable finite difference approximations of convection–diffusion equations lead to large sparse linear systems of equations whose coefficient matrix is an M-matrix, which is highly non-symmetric when the convection dominates. For an efficient iterative solution of such systems, it is proposed to consider in the non-symmetric case an algebraic multilevel preconditioning method formerly proposed f...

We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin (DG) discretization for convection terms, and a mixed method using H(div) spaces for the diffusive terms. Furthermore, hybridization is used to reduce the number of globally coupled degrees of free...