New substructuring domain decomposition methods for advection-diffusion equations

Journal of Computational and Applied Mathematics

Volumn 116, Issue 2, 2000, Pages 201-220

  Berselli, Luigi C ^a   Saleri, Fausto ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

Advection diffusion equations; Domain decomposition; Substructuring

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

ADVECTION-DIFFUSION EQUATION; DOMAIN DECOMPOSITION METHOD; STEKLOV-POINCARE OPERATORS;

COMPUTATIONAL METHODS;

ADVECTION; DIFFUSION; MATHEMATICAL METHOD;

EID: 0034655498     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00317-9     Document Type: Article

References (24)

1. Achdou Y., Nataf F. A Robin-Robin preconditioner for an advection-diffusion problem. C.R. Acad. Sci. Paris Sér. I Math. 325(11):1997;1211-1216.
2. R.A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press, New York, 1975.
3. Alonso A., Trotta R.L., Valli A. Coercive domain decomposition algorithms for advection diffusion equations and systems. J. Comp. Appl. Math. 96:1998;51-76.
4. A. Auge, A. Kapurkin, G. Lube, F.C. Otto, A note on domain decomposition of singularly perturbed elliptic problems in: P. Bj ø rstad, M. Espedal, D. Keyes (Eds.), Proceedings of the Ninth International Conference on Domain Decomposition Methods, Ullensvang, Norway, June 3-8, 1996, Wiley, New York, 1996.
5. L.C. Berselli, Multi-domain methods of Schwarz and Neumann-Neumann type for non-symmetric elliptic equations, in preparation.
6. Bramble J.H., Pasciak J.E., Schatz A.H. An iterative method for elliptic problems on regions partitioned into substructures. Math. Comp. 46(174):1986;361-369.
7. X.-C. Cai, An additive Schwarz algorithm for nonselfadjoint elliptic equations, in: T.F. Chan, R. Glowinski, J. Periaux, O.B. Widlund (Eds.), Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, Houston, TX, 1989, SIAM, Philadelphia, PA, 1990, pp. 232-244.
8. Cai X.-C. Additive Schwarz algorithms for parabolic convection-diffusion equations. Numer. Math. 60(1):1991;41-61.
9. Cai X.-C., Widlund O.B. Domain decomposition algorithms for indefinite elliptic problems. SIAM J. Sci. Statist. Comput. 13(1):1992;243-258.
10. C. Carlenzoli, A. Quarteroni, Adaptive domain decomposition methods for advection-diffusion problems, in: I. Babuška et al. (Eds.), Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, Minneapolis, MN, 1993, IMA Vol. Math. Appl., Vol. 75, Springer, New York, 1995, pp. 165-186.
11. C. Carlenzoli, A. Quarteroni, Adaptive domain decomposition methods for advection-diffusion problems, in: I. Babuška et al. (Eds.), Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, Minneapolis, MN, 1993, IMA Vol. Math. Appl., Vol. 75, Springer, New York, 1995, pp. 165-186.
12. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, New York, 1978.
13. Dryja M., Widlund O.B. Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems. Comm. Pure Appl. Math. 48(2):1995;121-155.
14. Gastaldi F., Gastaldi L., Quarteroni A. Adaptive domain decomposition methods for advection dominated equations. East-West J. Numer. Math. 4(3):1996;165-206.
15. Hughes T.J.R., Franca L.P., Hulbert G.M. A new finite element formulation for computational fluid dynamics. VIII. The Galerkin. / least-squares method for advective-diffusive equations Comput. Meth. Appl. Mech. Engng. 73(2):1989;173-189.
16. Le Tallec P. Domain decomposition methods in computational mechanics. Comput. Mech. Adv. 1(2):1994;121-220.
17. Marini L.D., Quarteroni A. A relaxation procedure for domain decomposition methods using finite elements. Numer. Math. 55(5):1989;575-598.
18. Nataf F., Rogier F. Factorization of the convection-diffusion operator and the Schwarz Algorithm. Math. Models Meth. Appl. Sci. 5:1995;67-93.
19. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967.
20. J.S. Przemieniecki, Theory of Matrix Structural Analysis (reprint of McGraw-Hill, 1968 Edition) McGraw Hill, Dover, NY, 1985.
21. Quarteroni A., Sacchi-Landriani G., Valli A. Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements. Numer. Math. 59:1991;831-859.
22. A. Quarteroni, A. Valli, Domain decomposition methods for partial differential equations, Oxford Univ. Press, Oxford, 1999.
23. H.A. Schwarz, Gesammelte Mathematische Abhandlungen, Vol. 2, Springer, Berlin, 1890, pp. 133-143.
24. O.B. Widlund, Some Schwarz methods for symmetric and nonsymmetric elliptic problems, in: T.F. Chan, G.A. Meurant, J.S. Scroggs, R.G. Voigt (Eds.), Proceeding of the Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Norfolk, VA, 1991, SIAM, Philadelphia, PA, 1992, pp. 19-36.