Fractional space-time variational formulations of (Navier-) Stokes equations
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Date
2015-12Type
- Report
ETH Bibliography
yes
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Abstract
Well-posed space-time variational formulations in fractional order Bochner-Sobolev spaces are proposed for parabolic partial differential equations, and in particular for the instationary Stokes andNavier-Stokes equations on bounded Lipschitz domains. The latter formulations include the pressure variable as a primal unknown, and so account for the incompressibility constraint via a Lagrange multiplier. The proposed new variational formulations can be the basis of adaptive numerical solution methods that converge with the best possible rate, which, by exploiting the tensor product structure of a Bochner space, equals the rate of best approximation for the corresponding stationary problem. Unbounded time intervals are admissible in many cases, permitting an optimal adaptive solution of long-term evolution problems. Show more
Publication status
publishedJournal / series
Research ReportVolume
Publisher
Seminar für Angewandte Mathematik, ETHOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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ETH Bibliography
yes
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