A Posteriori Error Analysis of Component Mode Synthesis for the Frequency Response Problem

We consider the frequency response problem and derive a posteriori error estimates for the discrete error in a reduced finite element model obtained using the component mode synthesis (CMS) method. We provide estimates in a linear quantity of interest and the energy norm. The estimates reflect to what degree each CMS subspace influence the overall error in the reduced solution. This enables automatic error control through adaptive algorithms that determine suitable dimensions of each subspace. We illustrate the theoretical results by including several numerical examples.