Certified real-time solution of parametrized partial differential equations

Engineering analysis requires the prediction of (say, a single) selected ?output? se relevant to ultimate component and system performance. Typical outputs include energies and forces, critical stresses or strains, flowrates or pressure drops, and various local and global measures of concentration, temperature, and flux. These outputs are functions of system parameters, or ?inputs?, ?, that serve to identify a particular realization or configuration of the component or system. These inputs typically reflect geometry, properties, and boundary conditions and loads; we shall assume that ? is a P-vector (or P-tuple) of parameters in a prescribed closed input domain D ? ?p. The input-output relationship se(?) D ? ? thus encapsulates the behavior relevant to the desired engineering context.