A posteriori error estimation for POD-based reduced order modelling with application in homogenisation

Overview & Synopsis

In this paper, we present an upper bounding technique for reduced order modelling applied to homogenisation. The error estimate relies on the construction of a reduced model for the stress field. Upon ensuring that the reduced stress satisfies the equilibrium in the finite element sense, we can indeed obtain the desired bounding property. We show that the sharpness of the estimate can be seamlessly controlled by changing the parameters of the reduced order model for the stress field.