Lyapunov-Based Error Bounds for the Reduced-Basis Method

We introduce two new error bounds for the reduced-basis method. Existing error bounds for parabolic problems can be classified as either space time or time stepping. Space-time bounds are much more costly and often become unpractical. The cheaper times-stepping bounds have always failed to adequately represent the dynamics of systems containing noncoercive operators. As a result they have always produced extremely pessimistic bounds. Our new bounds are time-stepping bounds that make use of the Lyapunov stability theory to better capture the dynamics of the system.