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Hughes, Thomas J. R.; Stewart, James R.

A space-time formulation for multiscale phenomena. (English) Zbl 0869.65061

J. Comput. Appl. Math. 74, No. 1-2, 217-229 (1996).
Authors’ summary: We develop subgrid scale models for a class of nonsymmetric, linear evolution operators by applying the variational multiscale method in space-time. The results generalize those of T. J. R. Hughes [Comput. Methods Appl. Mech. Eng. 127, No. 1-4, 387-401 (1995; Zbl 0866.76044)] which were confined to the steady case. The subgrid scale models are shown to be a paradigm for “bubble” function finite element methods and provide a theoretical and practial framework for the development of so-called stabilized methods.
Reviewer: H.Marcinkowska (Wrocław)

Cited in 64 Documents

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations

Keywords:

bubble function finite element methods; linear evolution operators; multiscale method; stabilized methods

Citations:

Zbl 0866.76044
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\textit{T. J. R. Hughes} and \textit{J. R. Stewart}, J. Comput. Appl. Math. 74, No. 1--2, 217--229 (1996; Zbl 0869.65061)
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References:

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