CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
UNIVERSITY OF COLORADO AT DENVER
TITLE: Optimal approximability of solutions of singularly
perturbed differential equations.
SPEAKER: Martin Stynes, Department of Mathematics,
University College Cork, Ireland
DATE: Monday, September 15, 1997
PLACE: Math Conference Room 626
UCD Building, 1250 14th St., Denver
TIME: noon (Refreshments served at 11:45 am)
ABSTRACT
We consider linear singularly perturbed convection-diffusion and
reaction-diffusion problems. While many numerical methods have been applied to
solve such problems, little attention has been paid to the optimality (or
otherwise) of these methods in terms of the smoothness of the solution of the
problem and of the value of the singular perturbation parameter; small values
of this parameter often cause a significant deterioration in the accuracy of a
computed solution. Using the theory of $n$-widths, we clarify the best possible
rates of convergence that can be attained in the $L_2$ norm.