A LOCAL L(2)-ERROR ANALYSIS OF THE STREAMLINE DIFFUSION METHOD FOR NONSTATIONARY CONVECTION-DIFFUSION SYSTEMS

We consider the discretization of linear, nonstationary, convection-do minated, convection-diffusion systems by the streamline diffusion fini te element method and give local error estimates in the energy norm fo r both linear scalar equations in arbitrary dimensions and for systems in one space dimension. For piecewise linear shape functions in time- space that are continuous in space and discontinuous in time, we obtai n optimal local error estimates of order O(h(3/2)) in those strip regi ons parallel to the streamline direction in which the exact solution i s smooth.