THE VARIATIONAL MULTISCALE METHOD - A PARADIGM FOR COMPUTATIONAL MECHANICS

We present a general treatment of the variational multiscale method in the context of an abstract Dirichlet problem. We show how the exact t heory represents a paradigm for subgrid-scale models and a posteriori error estimation. We examine hierarchical p-methods and bubbles in ord er to understand and, ultimately, approximate the 'fine-scale Green's function' which appears in the theory. We review relationships between residual-free bubbles, element Green's functions and stabilized metho ds. These suggest the applicability of the methodology to physically i nteresting problems in fluid mechanics, acoustics and electromagnetics . (C) 1998 Elsevier Science S.A. All rights reserved.