Necessary L2-uniform convergence conditions for difference schemes for two-dimensional convection-diffusion problems

AbstractWe derive necessary conditions for the uniform convergence (with respect to the perturbation parameter) in L2 of schemes for singularly perturbed convection-diffusion problems. Applying these conditions, we show that the convergence order of the streamline diffusion finite element method with piecewise linear trial functions cannot be better than 12, uniformly in the singular perturbation parameter