A generalized empirical interpolation method: Application of reduced basis techniques to data assimilation

Abstract

This paper, written as a tribute to Enrico Magenes, a giant that has kindly and warmly supported generations of young researchers, introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound information from data and reconstruct information, possibly taking into account noise in the acquisition, that can serve as an input to models expressed by partial differential equations. The approach combines data acquisition (with noise) with domain decomposition techniques and reduced basis approximations.