Stabilized Schemes for the Hydrostatic Stokes Equations

Statistics
Metrics and citations
Share
Metadata
Show full item recordDate
2005-01-01Department
MatemáticasSource
SIAM J. Numer. Anal., 53(4), 1876–1896Abstract
Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes
system or primitive equations of the ocean. It is known that the stability of the mixed formulation ap-
proximation for primitive equations requires the well-known Ladyzhenskaya–Babuˇska–Brezzi condi-
tion related to the Stokes problem and an extra inf-sup condition relating the pressure and the vertical
velocity.
The main goal of this paper is to avoid this extra condition by adding a residual stabilizing term to the
vertical momentum equation. Then, the stability for Stokes-stable FE combinations is extended to
the primitive equations and some error estimates are provided using Taylor–Hood P2 –P1 or miniele-
ment (P1 +bubble)–P1 FE approximations, showing the optimal convergence rate in the P2 –P1 case.
These results are also extended to the anisotropic (nonhydrostatic) problem. On the other hand,
by adding another residual term to the continuity equation, a better approximation of the vertical
derivative of pressure is obtained. In this case, stability and error estimates including this better
approximation are deduced, where optimal convergence rate is deduced in the (P 1 +bubble)–P1 case.
Finally, some numerical experiments are presented supporting previous results.
Subjects
inf-sup condition; incompressible fluids; hydrostatic pressure; primitive equations; finite elements; stabilized schemesCollections
- Artículos Científicos [4817]
- Articulos Científicos Matemáticas [161]