Stability and error analysis for a spectral Galerkin method for the Navier‐Stokes equations with  H  2  or  H  1  initial data | Zendy

He Yinnian | Zendy

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Stability and error analysis for a spectral Galerkin method for the Navier‐Stokes equations with H 2 or H 1 initial data

Author(s) -

He Yinnian

Publication year - 2005

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.20065

Subject(s) - mathematics , galerkin method , backward euler method , interval (graph theory) , euler's formula , mathematical analysis , stability (learning theory) , spectral method , convergence (economics) , rate of convergence , partial differential equation , euler equations , finite element method , physics , combinatorics , channel (broadcasting) , machine learning , computer science , economics , thermodynamics , economic growth , engineering , electrical engineering

In this article we consider a spectral Galerkin method with a semi‐implicit Euler scheme for the two‐dimensional Navier‐Stokes equations with H 2 or H 1 initial data. The H 2 ‐stability analysis of this spectral Galerkin method shows that for the smooth initial data the semi‐implicit Euler scheme admits a large time step. The L 2 ‐error analysis of the spectral Galerkin method shows that for the smoother initial data the numerical solution u m nexhibits faster convergence on the time interval [0, 1] and retains the same convergence rate on the time interval [1, ∞). © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.

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