by Tobiska, L..
Series: 2005-36, Preprints
We consider a singularly perturbed advection-diffusion two-point boundary value problem whose solution has a single boundary layer. Based on piecewise polynomial approximations of degree $k\ge 1$, a new stabilized finite element method is derived in the framework of a variational multiscale approach. The method coincides with the SUPG method for $k=1$ but differs from it for $k\ge 2$. Estimates for the error to an appropriate interpolant are given in several norms on different types of meshes. For $k=1$ enhanced accuracy is achieved by superconvergence. Postprocessing guarantees the same estimates for the error to the solution itself.
stabilized finite element method, singular perturbation, advection-diffusion, Shishkin mesh, superconvergence, postprocessing