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Negative norm least-squares methods for the velocity-vorticity-pressure Navier–Stokes equations

✍ Scribed by Pavel B. Bochev

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
378 KB
Volume
15
Category
Article
ISSN
0749-159X

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✦ Synopsis

We develop and analyze a least-squares finite element method for the steady state, incompressible Navier-Stokes equations, written as a first-order system involving vorticity as new dependent variable. In contrast to standard L 2 least-squares methods for this system, our approach utilizes discrete negative norms in the least-squares functional. This allows us to devise efficient preconditioners for the discrete equations, and to establish optimal error estimates under relaxed regularity assumptions.

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