Optimal approximability of solutions of singularly perturbed differential equations

Prof. R. Bruce Kellogg

Institute for Physical Science and Technology and Department of Mathematics, University of Maryland

Using the theory of n-widths, the approximability of solutions of singularly perturbed reaction-diffusion and convection-diffusion problems in one dimension is quantified. The results lead to conjectures regarding finite element methods for singular perturbation problems, and for the analysis of singular perturbation problems themselves.