Error Estimates for the Spectral Approximation of the Nonstationary Stokes Problem

Error Estimates for the Spectral Approximation of the Nonstationary Stokes Problem

This paper analyzes a discretization of the nonstationary Stokes problem with periodic-nonperiodic boundary conditions. Fourier-Legendre spectral approximations are considered with respect to the space variables, while the time discretization is based on the second-order, Crank-Nicolson scheme. Opti...

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Veröffentlicht in:SIAM journal on numerical analysis 1990-10, Vol.27 (5), p.1160-1186
Hauptverfasser: Landriani, Giovanni Sacchi, Vandeven, Herve
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Banach spaces
Boundary conditions
Degrees of polynomials
Estimates
Exact sciences and technology
Inner products
Integers
Mathematics
Methods
Navier Stokes equation
Norms
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Polynomials
Real numbers
Sciences and techniques of general use
Spectral methods
Textual collocation
Velocity
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Beschreibung
Zusammenfassung:This paper analyzes a discretization of the nonstationary Stokes problem with periodic-nonperiodic boundary conditions. Fourier-Legendre spectral approximations are considered with respect to the space variables, while the time discretization is based on the second-order, Crank-Nicolson scheme. Optimal convergence estimates are proved for the velocity field.
ISSN:0036-1429
1095-7170
DOI:10.1137/0727067