A reduced basis method for the wave equation

Abstract

In this contribution, we derive an a posteriori error estimator for the second-order wave equation motivated by energy-based a priori estimates by Bernardi and Süli [“Time and Space Adaptivity for the Second-order Wave Equation.” Mathematical Models and Methods in Applied Sciences 15 (2): 199–225]. This estimate (which is valid for general discretisations) is then used to derive a POD-Greedy reduced basis approach for the parameterised wave equation. The quantitative performance of the online-efficient error estimator is shown for an illustrative example, keeping in mind that model reduction of parametrised hyperbolic problems is a challenge.