A stabilized Galerkin method for convection dominated diffusion problems

摘要

We describe a new method for solving convection dominated diffusion problems. The idea of the method is that the standard unstable symmetric (or Bubnov—Galerkin) finite-element discretization can be stabilized by a suitable extension of the test space. This results in an overdetermined linear system, to be solved in least squares sense. Both QR-factorization and preconditioned conjugate gradients applied to the normal equations are feasible as solution method. Although the discretization is derived by a conforming method, the normal equations show resemblance to a discretization by the (nonconforming) streamline-upwind/Petrov—Galerkin method. We shall display a number of examples and a comparison to SU/PG.