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Convergence analysis of domain decomposition algorithms with full overlapping for the advection-diffusion problems


Authors: P. Le Tallec and M. D. Tidriri
Journal: Math. Comp. 68 (1999), 585-606
MSC (1991): Primary 65Jxx, 65M12, 65C20, 76Nxx, 82Cxx
DOI: https://doi.org/10.1090/S0025-5718-99-01030-3
MathSciNet review: 1613715
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Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to study the convergence properties of a time marching algorithm solving advection-diffusion problems on two domains using incompatible discretizations. The basic algorithm is first described, and theoretical and numerical results that illustrate its convergence properties are then presented.


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  • 1. J.-F. Bourgat, P. Le Tallec and M. D. Tidriri, Coupling Boltzman and Navier-Stokes equations by friction, J. Comp. Phy. 127, 227-245 CMP 98:09 (1996).
  • 2. M.O. Bristeau, R. Glowinski, L. Dutto, J. Périaux, G. Rogé, Compressible viscous flow calculations using compatible finite element approximations, 7th Int. Conf. on Finite Element Methods in Flow Problems, Huntsville, Alabama (1989) ; et International Journal for Numerical Methods in Fluids 11 (1990), pp. 719-749. MR 91g:76062
  • 3. R. Glowinski, G. Golub, G. A. Meurant and J. Périaux (eds), Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Paris, France, January 7-9, 1987, (SIAM, Philadelphia, 1988). MR 89f:65005
  • 4. T. Chan, R. Glowinski, J. Périaux and O. Widlund (eds), Proceedings of the Second International Symposium on Domain Decomposition Methods for Partial Differential Equations, Los Angeles, California, January 14-16, 1988, (SIAM, Philadelphia, 1989). MR 89j:65010
  • 5. T. Chan, R. Glowinski, J. Périaux and O. Widlund (eds), Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, Houston, Texas, March 20-22, 1989, (SIAM, Philadelphia, 1990). MR 91e:65010
  • 6. R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux and O. Widlund (eds), Proceedings of the Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Moscow, May 21-25, 1990, (SIAM, Philadelphia, 1991). MR 92a:65023
  • 7. T. Chan, D. Keyes, G. Meurant, J. Scroggs and R. Voigt (eds), Proceedings of the Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Norfolk, Virginia, May 6-8, 1991, (SIAM, Philadelphia, 1992). MR 93g:65009
  • 8. A. Quarteroni (ed), Proceedings of the Sixth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Como, June 15-19, 1992, Contemp. Math. 157 (AMS, Providence, 1994). MR 94i:65004
  • 9. Y. Achdou and O. Pironneau, A fast solver for Navier-Stokes equations in the laminar regime using mortar finite element and boundary element methods, Technical Report 93-277 (Centre de Mathématiques Appliquées, Ecole Polytechnique, Paris, 1993).
  • 10. C. Canuto and A. Russo, On the Elliptic-Hyperbolic Coupling. I: The Advection Diffusion Equation via the $\xi$-formulation, Math. Models and Meth. Appl. Sciences 3 (1993), no. 2, 145-170. MR 94e:65130
  • 11. Cercignani, C., Theory and application of the Boltzmann equation, Springer, (1988).
  • 12. P. Le Tallec and M. D. Tidriri, Convergence Analysis of Domain Decomposition Algorithms with Full Overlapping for the Advection-Diffusion Problems. Rapport de recherche INRIA no 2435, Octobre 1994 (57 pages).
  • 13. P. Le Tallec and M. D. Tidriri, Analysis of the explicit time marching algorithm. ICASE Report No. 96-45.
  • 14. L. Marini and A. Quarteroni, An iterative procedure for domain decomposition methods: a finite element approach. In [3] 129-143. MR 90d:65196
  • 15. L. D. Marini and A. Quarteroni, A relaxation procedure for domain decomposition methods using Finite Elements, Numer. Math. 55, (1989) 575-598. MR 90g:65150
  • 16. A. Quarteroni, G. Sacchi Landriani and A Valli, Coupling of Viscous and Inviscid Stokes Equations via a Domain Decomposition Method for Finite Elements, Technical report UTM89-287 (Dipartimento di Mathematica, Universita degli Studi di Trento, 1989).
  • 17. Ph. Rostand, B. Stoufflet, Finite volume Galerkin methods for viscous gas dynamics, Rapport de recherche INRIA no 863, Juillet 1988.
  • 18. M. D. Tidriri, Couplage d'approximations et de modèles de types différents dans le calcul d'écoulements externes, PhD thesis, University of Paris IX, 1992. MR 96d:65202
  • 19. M. D. Tidriri, Domain Decomposition for Incompatible Nonlinear Models. INRIA Research Report RR-2378, October 1994.
  • 20. M. D. Tidriri, Domain decomposition for compressible Navier-Stokes equations with different discretizations and formulations. J. Comp. Phy. 119, 271-282 (1995). CMP 98:09
  • 21. Y. A. Kuznetsov, Overlapping Domain Decomposition Methods for Parabolic Problems. In [8]. CMP 94:08
  • 22. H. Blum, S. Lisky and R. Rannacher, A domain decomposition algorithm for parabolic problems, Preprint 02-08, Interdisziplinaeres Zentrum fuer Wissenschaftliches Rechen, Universitaet Heidelberg, 1992; A domain splitting algorithm for parabolic problems, Computing 49 (1992), 11-23; MR 93f:65071

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Additional Information

P. Le Tallec
Affiliation: INRIA, Domaine de Voluceau Rocquencourt, B.P. 105, Le Chesnay Cedex, France
Email: Partrick.LeTallec@inria.fr

M. D. Tidriri
Affiliation: Iowa State University, Department of Mathematics, 400 Carver Hall, Ames, IA 50011
Email: tidriri@iastate.edu

DOI: https://doi.org/10.1090/S0025-5718-99-01030-3
Received by editor(s): January 11, 1995
Received by editor(s) in revised form: April 5, 1996, and November 21, 1996
Additional Notes: This work has been supported by the Hermes Research program under grant number RDAN 86.1/3. The second author was also supported by the National Science Foundation under contract number ECS-8957475 and by the United Technologies Research Center while he was at Yale University.
Article copyright: © Copyright 1999 American Mathematical Society

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