A posteriori error estimation and adaptivity for temporal multiscale problems

Abstract In science and engineering, problems over multiple scales in time often arise. Two examples are material damage in oscillating structures or plaque growth in pulsating blood vessels. Here the long term effects are of interest but they depend on the coupled fast‐changing physical processes which must be taken into account. One method to efficiently simulate these problems is to split them into an averaged slow scale process and a localized fast scale process. We apply the dual weighted residual method on a generalized formulation for this type of problem to obtain an error estimator which can be used for adaptive refinement. Special care must be taken to separate the slow scale and fast scale influences on the estimator.