AN EFFICIENT OUTPUT ERROR ESTIMATION FOR MODEL ORDER REDUCTION OF PARAMETRIZED EVOLUTION EQUATIONS

In this work we present an a posteriori output error bound for model order reduction of parametrized evolution equations. With the help of the dual system and a simple representation of the relationship between the field variable error and the residual of the primal system, a sharp output error bound is derived. Such an error bound successfully avoids the accumulation of the residual over time, which is a common drawback in the existing error estimations for time-stepping schemes. An estimation needs to be performed for practical computation of the error bound, and as a result, the output error bound reduces to an output error estimation. The proposed error estimation is applied to four kinds of problems. The first one is a linear convection-diffusion equation, which is used to compare the performance of the new error estimation and an existing primal-dual error bound. The second one is the unsteady viscous Burgers' equation, an academic benchmark of nonlinear evolution equations in fluid dynamics often used as a first test case to validate nonlinear model order reduction methods. The other two problems arise from chromatographic separation processes. Numerical experiments demonstrate the performance and efficiency of the proposed error estimation. Furthermore, optimization based on the resulting reduced-order models is successful in terms of accuracy and runtime for obtaining the optimal solution.