The variational multiscale method—a paradigm for computational mechanics Original Research Article

We present a general treatment of the variational multiscale method in the context of an abstract Dirichlet problem. We show how the exact theory represents a paradigm for subgrid-scale models and a posteriori error estimation. We examine hierarchical p-methods and bubbles in order to understand and, ultimately, approximate the ‘fine-scale Greenʹs function’ which appears in the theory. We review relationships between residual-free bubbles, element Greenʹs functions and stabilized methods. These suggest the applicability of the methodology to physically interesting problems in fluid mechanics, acoustics and electromagnetics.