zbMATH — the first resource for mathematics

Application of maximum principles to the analysis of a coupling time marching algorithm. (English) Zbl 0922.35029
Summary: We study the convergence properties of a coupling time marching algorithm solving convection-diffusion problems on two domains using incompatible approximations. Convergence properties are obtained using local and global estimates of the solutions of convection-diffusion problems. \(\copyright\) Academic Press.

35B50 Maximum principles in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
Full Text: DOI
[1] Y. Achdou, O. Pironneau, A Fast Solver for Navier-Stokes Equations in the Laminar Regime Using Mortar Finite Element and Boundary Element Methods, 93-277, Centre de Mathématiques Appliquées, Ecole Polytechnique, Paris, 1993 · Zbl 0833.76032
[2] Aleksandrov, A.D., Majoration of solutions of second order linear equations, Vestnik leningrad univ., 21, 5-25, (1966)
[3] Bakel’man, I.Y., Theory of quasilinear elliptic equations, Siberian math. J., 2, 179-186, (1961)
[4] M. O. Bristeau, R. Glowinski, L. Dutto, J. Périaux, G. Rogé, Compressible viscous flow calculations using compatible finite element approximations, Seventh International Conference on Finite Element Methods in Flow Problems, Huntsville, Alabama, 1989, Internat. J. Numer. Methods Fluids, \bf11
[5] Canuto, C.; Russo, A., On the elliptic-hyperbolic coupling. I: the advection diffusion equation via the ξ-formulation, Math. models meth. appl. sci., 3, 145-170, (1993) · Zbl 0773.76066
[6] Cercignani, C., Theory and application of the Boltzmann equation, (1988), Springer-Verlag Berlin/New York
[7] Gilbarg, D.; Trudinger, N.S., Elliptic partial differential equations of second order, (1977), Springer-Verlag Berlin-Heidelberg-New York · Zbl 0691.35001
[8] Bourgat, J.F.; Le Tallec, P.; Mallinger, F.; Qiu, Y.; Tidriri, M.D., Numerical coupling of Boltzmann and navier – stokes, Proceedings of the sixth I.U.T.A.M. (international union of theoretical and applied mechanics) conference on rarefied flows for reentry problems, Marseille, France, (Sept. 1992)
[9] Bourgat, J.-F.; Le Tallec, P.; Tidriri, M.D., Coupling navier – stokes and Boltzmann, J. comput. phys., 127, 227-245, (1996) · Zbl 0860.76080
[10] Le Tallec, P.; Mallinger, F., Coupling Boltzmann and navier – stokes equations by half fluxes, J. comput. phys., 136, 51-67, (1997) · Zbl 0890.76042
[11] P. Le Tallec, M. D. Tidriri, Convergence Analysis of Domain Decomposition Algorithms with Full Overlapping for the Advection-Diffusion Problems, 96-37, 1996, Math. Comp.
[12] A. Quarteroni, G. S. Landriani, A. Valli, Coupling of Viscous and Inviscid Stokes Equations via a Domain Decomposition Method for Finite Elements, UTM89-287, Dipartimento di Mathematica, Universita degli Studi di Trento, 1989 · Zbl 0724.76049
[13] P. Rostand, B. Stoufflet, Finite Volume Galerkin Methods for Viscous Gas Dynamics, 863, Juillet, 1988 · Zbl 0661.76073
[14] M. D. Tidriri, Couplage d’Approximations et de Modèles de Types Différents dans le Calcul d’écoulements Externes, Université de Paris IX, 1992
[15] M. D. Tidriri, Domain Decomposition for Incompatible Nonlinear Models, 2435, Dec. 1994
[16] Tidriri, M.D., Domain decompositions for compressible navier – stokes equations, J. comput. phys., 119, 271-282, (1995) · Zbl 0834.76071
[17] Tidriri, M.D., Local and global estimates for the solutions of convection – diffusion problems, J. math. anal. appl., 29, 137-157, (1999) · Zbl 0924.35046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.