%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 }