THE CHARACTERISTIC STREAMLINE DIFFUSION FINITE-ELEMENT METHOD

We present a variant of the Streamline diffusion finite element method for time-dependent convection-diffusion problems with space-time elements approximately oriented along the characteristics in space-time. For the resulting method, which is referred to as the Characteristic Streamline Diffusion method (CSD-method for short), we prove a posteriori and a priori error estimates indicating that the CSD-method has the advantage of a method of characteristics in that large time steps may be taken without destroying accuracy. Adaptive implementations based on the a posteriori error estimates are briefly discussed and some numerical results are also reported.