Reduced Basis Output Bounds Methods: Fast and Reliable Approximations
and some Applications.

After a brief example to motivate the methodology, I present an overview of
the reduced basis output bounds methods. In particular,
I will present (i) an algorithm for an adaptive approximation which could be
constrained by accuracy or computing time and (ii) some ingredients for the
application of these methods to the viscous Burgers equation and how it can
be extended to the incompressible Navier Stokes equations.