Analysis of a new stabilized higher order finite element method for advection–diffusion equations

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 ⩾ 1, a new stabilized finite element method is derived in the framework of a variation multiscale approach. The method coincides with the SUPG method for k = 1 but differs from it for k ⩾ 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.