A Spectral Element Method for the Navier--Stokes Equations with Improved Accuracy

Authors:
Javier de Frutos;Julia Novo
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 2

Postprocessing Fourier spectral methods: the case of smooth solutions

Applied Numerical Mathematics
A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations

Journal of Computational and Applied Mathematics

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Abstract

We present a procedure to enhance the accuracy of spectral element methods for the evolutionary Navier--Stokes equations. The approximations to the velocity and the pressure obtained using a spectral element method are postprocessed by solving a discrete Stokes problem only once, when the time evolution is completed. The analysis shows that this procedure improves the order of convergence for the approximations to the velocity and the pressure. The choice of a discrete pressure space endowed with an inf-sup condition independent of the discretization parameter leads to optimal error bounds for the pressure.