Analysis of time discretization of incompressible Navier-Stokes problem (Q2744663)
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scientific article; zbMATH DE number 1652866
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analysis of time discretization of incompressible Navier-Stokes problem |
scientific article; zbMATH DE number 1652866 |
Statements
30 September 2001
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incompressible Navier-Stokes equations
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implicit time discretization
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implicit Euler scheme
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second-order backward differencing scheme
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convergence
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higher-order error estimates
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regularity
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functional analysis
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stability
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Analysis of time discretization of incompressible Navier-Stokes problem (English)
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The text deals with a rigorous mathematical analysis of implicit time discretizations for incompressible Navier-Stokes equations. The major focus is spent to the implicit Euler scheme and to a second-order backward differencing scheme. For the latter new convergence results as well as new higher-order error estimates are obtained under moderate regularity assumptions. Also the necessary framework of functional analysis required for deriving the results is briefly recapitulated. For readers who are interested in theoretical mathematical properties of time discretizations for incompressible flows, the book provides a well-founded and comprehensive resource for various issues related to the subject (i.e. solvability, stability, convergence, error estimation).
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