RT journal article
T1 Stabilized Schemes for the Hydrostatic Stokes Equations
A1 Rodríguez Galván, José Rafael
A1 Guillén González, Francisco
A2 Matemáticas
K1 inf-sup condition
K1 incompressible fluids
K1 hydrostatic pressure
K1 primitive equations
K1 finite elements
K1 stabilized schemes
AB Some new stable finite element (FE) schemes are presented for the hydrostatic Stokessystem 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 verticalvelocity.The main goal of this paper is to avoid this extra condition by adding a residual stabilizing term to thevertical momentum equation. Then, the stability for Stokes-stable FE combinations is extended tothe 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 verticalderivative of pressure is obtained. In this case, stability and error estimates including this betterapproximation are deduced, where optimal convergence rate is deduced in the (P 1 +bubble)–P1 case.Finally, some numerical experiments are presented supporting previous results.
PB Society for Industrial and Applied Mathematics
YR 2005
FD 2005-01-01T00:00:00Z
LK http://hdl.handle.net/10498/17959
UL http://hdl.handle.net/10498/17959
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026