Stabilized finite element methods for singularly perturbed parabolic problems Original Research Article

We consider two stabilized numerical schemes for solving initial/boundary value problems of parabolic equations modelling convection-diffusion-reaction. Weighted least-squares forms of the underlying equation are added to the basic Galerkin finite element semidiscretization in order to accomodate the method to (possibly locally varying) convective, reactive or diffusive terms. Time integration is performed with standard stable one-step methods. We derive stability and error estimates on unstructured grids and consider the design of the numerical damping parameters. Numerical results are given for typical model problems. In a subsequent paper we extend the method to the incompressible Navier-Stokes problem.