Multigrid methods for convection–diffusion problems discretized by a monotone scheme

We study multigrid (MG) methods for the solution of systems of linear algebraic equations obtained from a stable discretization of convection–diffusion problems by an exponential fitting scheme. The latter ensures the stability of the simplest possible coarse grid operators obtained from Galerkin projections based on graph matching. Linear and nonlinear MG preconditioners are defined in the framework of algebraic multilevel iteration. The option of using polynomial smoothers is investigated in context of nonsymmetric problems and a systematic performance comparison is presented for various algorithms on a representative set of two- and three-dimensional test problems. •We consider stationary convection-diffusion-reaction equations for 2D and 3D case.•For a stable discretization we choose a monotone exponential fitting scheme.•We solve the discrete system using linear and nonlinear algebraic multigrid methods.•Among different smoothers for the multigrid methods we use polynomial smoothers.•Systematic performance comparison reveals stable efficient options of our algorithm