Multigrid methods based on matrix-dependent coarse spaces for nonconforming streamline-diffusion finite element discretization of convection-diffusion problems (Q2708280)

This paper analyzes a nonconforming streamline-diffusion finite element method for solving convection-diffusion problems on rectangular meshes. This method uses the nonconforming quadrilateral finite elements introduced by \textit{R. Rannacher} and \textit{S. Turek} [Numer. Methods Partial Differ. Equations 8, No. 2, 97-111 (1992; Zbl 0742.76051)], combined with a construction of a pure algebraic multigrid procedure for the solution of the resulting discrete system.NEWLINENEWLINENEWLINEThe proposed multigrid method is employed as a preconditioner in the generalized conjugate gradient iterative method for solving the resulting nonsymmetric system of linear algebraic equations. Finally, some numerical experiments illustrate the performance of the method on a two-dimensional convection-diffusion model problem both in the convection-dominated and diffusion-dominated limits.