Improvement and generalization of a finite element shallow-water solver to multi-layer systems

International Journal for Numerical Methods in Fluids

Volumn 31, Issue 7, 1999, Pages 1037-1059

  Macías, Jorge ^a   Pares, Carlos ^a   Castro, Manuel J ^a  

^a UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Alboran Sea; Duality methods; FEM; Preconditioned; Shallow water equations

Indexed keywords

FINITE ELEMENT METHOD; ITERATIVE METHODS; MULTILAYERS; NONLINEAR EQUATIONS;

PRECONDITIONERS; SHALLOW WATER SOLVER;

COMPUTATIONAL FLUID DYNAMICS;

ESTUARINE DYNAMICS; FINITE ELEMENT METHOD; SHALLOW-WATER EQUATION; TIDAL FLOW;

EID: 0033571987     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19991215)31:7<1037::AID-FLD909>3.0.CO;2-V     Document Type: Article

References (19)

1. A. Bermúdez, C. Rodriguez and M.A. Vilar, 'Solving shallow water equations by a mixed implicit finite element method', IMA J. Numer. Anal, 11, 79-97 (1991).
2. A. Bermúdez and C. Moreno, 'Duality methods for solving variational inequalities', Comp. Maths. Appl., 7, 43-58 (1981).
3. O. Pironneau, Méthodes des Éléments Finis pour les Fluides, vol. 7 of RMA, Masson, Paris, 1988.
4. J.F. Rodrigues, Obstacle Problems in Mathematical Physics, North-Holland, Amsterdam, 1987.
5. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Studies in Mathematics and its Applications, vol. 1, North-Holland, Paris, 1976.
6. J. Macías, 'Some topics in numerical modelling in oceanography', PhD Thesis, University of Paris VI, Paris, 1998.
7. C. Pares, J. Macías and M.J. Castro, 'Duality methods with automatic choice of parameters. Application to shallow-water equations in conservative form', Internal Journal 0115, Group on Differential Equations, Numerical Analysis and Applications, University of Malaga, Spain, 1998; also submitted to Numerische Mathematik.
8. C. Pares, J. Macías and M.J. Castro, 'Duality methods with automatic choice of parameters. Application to shallow-water equations in conservative form', Internal Journal 0115, Group on Differential Equations, Numerical Analysis and Applications, University of Malaga, Spain, 1998; also submitted to Numerische Mathematik.
9. P.A. Raviart and J.M. Thomas, 'A mixed finite element method for 2nd order elliptic problems', in Mathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics, vol. 606, Springer, Berlin, 1977, pp. 292-313.
10. M.J. Castro, J. Macías and C. Parés, 'The design of an IC-type preconditioner. Description and applications', Internal Journal 0130, group on Differential Equations, Numerical Analysis and Applications, University of Malaga, Spain, 1998.
11. M.J. Castro and J. Macías, Modelo Matemático de las Corrientes Forzadas por el Viento en el Mar de Alborán, vol. 5, Publicaciones del Grupo de Análisis Matemático Aplicado de la Universidad de Málaga, 1994.
12. M.J. Castro, J. Macías and C. Pares, 'A multilayer shallow water model. Applications to the modelling of the Alboran Sea and the Strait of Gibraltar', in J.I. Díaz (ed.), The Mathematics of Models for Climatology and Environment, Heidelberg, Germany, 1996, pp. 367-394; NATO ASI Series I: Global Environmental Change, No. 48, Springer, New York.
13. M.J. Castro, J. Macías and C. Pares, 'A multilayer shallow water model. Applications to the modelling of the Alboran Sea and the Strait of Gibraltar', in J.I. Díaz (ed.), The Mathematics of Models for Climatology and Environment, Heidelberg, Germany, 1996, pp. 367-394; NATO ASI Series I: Global Environmental Change, No. 48, Springer, New York.
14. G.W. Heburn and P.E. La Violette, 'Variations in the structure of the anticyclonic gyres found in the Alboran Sea', J. Geophys. Res., 95, 1599-1613 (1990).
15. H. Bryden, J. Candela and T.H. Kinder, 'Exchange through the Strait of Gibraltar', Prog. Oceanogr., 33, 201-248 (1994).
16. J. Macías, 'Deduction of a boundary condition for the input flow through the Strait of Gibraltar by a conservation of the potential vorticity approach', Internal Journal 1027, group on Differential Equations, Numerical Analysis and Applications, University of Málaga, 1997.
17. P. Orenga, 'Un théorème d'existence de solutions d'un problème de shallow water', Arch. Rational Mech. Anal., 130, 183-204 (1995).
18. A. Pazy, On the asymptotic behaviour of iterates of nonexpansive mappings in Hilbert spaces', Israel J. Math., 26, 197-204 (1977).
19. H. Brézis, Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973.