Least-Squares Spectral Collocation for the Navier–Stokes Equations

Authors:
Wilhelm Heinrichs
Affiliations:
Universität Duisburg-Essen, Ingenieurmathematik, Universitätsstr. 3, D-45117 Essen, Germany. wheinric@ing-math.uni-essen.de
Venue:
Journal of Scientific Computing
Year:
2004

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Abstract

A least-squares spectral collocation formulation for the Navier–Stokes problem is presented. By this new approach the well known Babu˘ska–Brezzi condition can be avoided. Here we are able to employ polynomials of the same degree both for the velocity components and for the pressure. The collocation conditions and the boundary conditions lead to a overdetermined system which can be efficiently solved by least-squares. The solution technique will only involve symmetric positive definite linear systems. The numerical simulations confirm the usual exponential rate of convergence for the spectral scheme.