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 Green's function' which appears in the theory. We review relationships between residual-free bubbles, element Green's functions and stabilized methods. These suggest the applicability of the methodology to physically interesting problems in fluid mechanics, acoustics and electromagnetics.
%0 Journal Article
%1 hughes98:CMAME-166-3
%A Hughes, Thomas J. R.
%A Feijco, Gonzalo R.
%A Mazzei, Luca
%A Quincy, Jean B.
%D 1998
%J Computer Methods in Applied Mechanics and Engineering
%K usyd 76m10-finite-element-methods-in-fluid-mechanics 65n30-pdes-bvps-finite-elements 76q05-hydro-and-aero-acoustics 78m10-optics-electromagnetism-finite-element-method
%P 3--24
%R 10.1016/S0045-7825(98)00079-6
%T The Variational Multiscale Method---A Paradigm for Computational Mechanics
%U http://dx.doi.org/10.1016/S0045-7825(98)00079-6
%V 166
%X 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 Green's function' which appears in the theory. We review relationships between residual-free bubbles, element Green's functions and stabilized methods. These suggest the applicability of the methodology to physically interesting problems in fluid mechanics, acoustics and electromagnetics.
@article{hughes98:CMAME-166-3,
abstract = {{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 Green's function' which appears in the theory. We review relationships between residual-free bubbles, element Green's functions and stabilized methods. These suggest the applicability of the methodology to physically interesting problems in fluid mechanics, acoustics and electromagnetics.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Hughes, Thomas J. R. and Feijco, Gonzalo R. and Mazzei, Luca and Quincy, Jean B.},
biburl = {https://www.bibsonomy.org/bibtex/2c957603d9207c8473b35f747b4b06b65/gdmcbain},
citeulike-article-id = {2441690},
citeulike-linkout-0 = {http://dx.doi.org/10.1016/S0045-7825(98)00079-6},
doi = {10.1016/S0045-7825(98)00079-6},
interhash = {129ba56259d6cbca8742b28e40762453},
intrahash = {c957603d9207c8473b35f747b4b06b65},
journal = {Computer Methods in Applied Mechanics and Engineering},
keywords = {usyd 76m10-finite-element-methods-in-fluid-mechanics 65n30-pdes-bvps-finite-elements 76q05-hydro-and-aero-acoustics 78m10-optics-electromagnetism-finite-element-method},
pages = {3--24},
posted-at = {2008-02-28 10:10:33},
priority = {5},
timestamp = {2019-07-02T02:17:55.000+0200},
title = {{The Variational Multiscale Method---A Paradigm for Computational Mechanics}},
url = {http://dx.doi.org/10.1016/S0045-7825(98)00079-6},
volume = 166,
year = 1998
}