A variational approach for temporal multiscale problems and its application to adaptivity and optimization

Abstract

AbstractWe discuss a computational multiscale method for the efficient simulation and optimization of differential equations with multiple scales in time. The approach is based on isolating the influences of the fast scale by a local periodic‐in‐time assumption that allows for time‐stepping of the averaged slow scale with very large step sizes. For this approach we develop a variational formulation that gives easy access to the methodology of goal‐oriented error estimation and adaptivity as well as gradient based optimization.