Multiscale temporal integration

We study the application of the variational multiscale method to the problem of temporal integration. with the final goal of designing integration schemes that go beyond the classical notion of upwinding. We develop a formulation based on a mixed hybrid finite element method, where the fine scale mode problems automatically decouple at the element level without the need to resort to a localization assumption. We give general orthogonality conditions for the trial and test spaces that allow to construct hierarchical p methods. We test some simple ideas for the modeling of the unresolved scales, The resulting algorithms are analyzed using classical analytical measures. (C) 2002 Elsevier Science B.V. All rights reserved.