Stabilized Schemes for the Hydrostatic Stokes Equations
| Autor: | J. R. Rodríguez Galván, F. Guillén González |
|---|---|
| Přispěvatelé: | Matemáticas |
| Jazyk: | angličtina |
| Rok vydání: | 2005 |
| Předmět: |
Numerical Analysis
primitive equations Applied Mathematics Hydrostatic pressure Mathematical analysis Stability (probability) Finite element method law.invention Computational Mathematics Rate of convergence Incompressible flow law incompressible fluids stabilized schemes Primitive equations inf-sup condition hydrostatic pressure finite elements Hydrostatic equilibrium Anisotropy Mathematics |
| Zdroj: | SIAM J. Numer. Anal., 53(4), 1876–1896 RODIN. Repositorio de Objetos de Docencia e Investigación de la Universidad de Cádiz instname |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|