Bounding Stability Constants for Affinely Parameter-Dependent Operators
This work provides a theoretical advancement for practitioners of the reduced basis method, offering offline guarantees of stability, though the contribution is incremental.
The paper introduces new methods for bounding stability constants in the reduced basis method, enabling guaranteed stability over neighborhoods rather than just finite points, and extends the framework to Lyapunov stability of dynamical systems.
In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more than a finite number of points and to do that in the offline stage. We additionally show that Lyapunov stability of dynamical systems can be handled in the same framework.