Exponential Convergence of Online Enrichment in Localized Reduced Basis Methods

Online enrichment is the extension of a reduced solution space based on the solution of the reduced model. Procedures for online enrichment were published for many localized model order reduction techniques. We show that residual based online enrichment on overlapping domains converges exponentially. Furthermore, we present an optimal enrichment strategy which couples the global reduced space with a local fine space. Numerical experiments on the two dimensional stationary heat equation with high contrast and channels confirm and illustrate the results.