Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems

Abstract

Adaptive finite element methods for stationary convection-diffusion problems are designed and analyzed. The underlying discretization scheme is the Shock-capturing Streamline Diffusion method. The adaptive algorithms proposed are based on a posteriori error estimates for this method leading to <italic>reliable</italic> methods in the sense that the desired error control is guaranteed. A priori error estimates are used to show that the algorithms are <italic>efficient</italic> in a certain sense.