Error estimates for model order reduction of Burgers' equation

Burgers' equation is a nonlinear scalar partial differential equation, commonly used as a testbed for model order reduction techniques and error estimates. Model order reduction of the parameterized Burgers' equation is commonly done by using the reduced basis method. In this method, an error estimate plays a crucial rule in both accelerating the offline phase and quantifying the error induced after reduction in the online phase. In this study, we introduce two new estimates for this reduction error. The first error estimate is based on a Lur'e-type model formulation of the system obtained after the full-discretization of Burgers' equation. The second error estimate is built upon snapshots generated in the offline phase of the reduced basis method. The second error estimate is applicable to a wider range of systems compared to the first error estimate. Results reveal that when conditions for the error estimates are satisfied, the error estimates are accurate and work efficiently in terms of computational effort