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

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.

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

Citations:

Zbl 0866.76044
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References:

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