Summary
We introduce a differential system based on the coupling of the (Navier) Stokes equations and the Darcy equation for the modelling of the interaction between surface and subsurface flows. We formulate the problem as an interface problem and analyze the associated Steklov-Poincaré operator. We then propose a way of solving the coupled problem iteratively, based on a suitable splitting of the interface conditions, allowing the solution of two subproblems at each step.
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References
Bear, J. (1979): Hydraulics of groundwater. McGraw-Hill, New York
Brezzi, F. (1974): On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. Rev. Française Automat. Informat. Recherche Opérationnelle 8, 129–151
Brezzi, F., Fortin, M. (1991): Mixed and hybrid finite element methods. Springer, New York
Discacciati, M., Miglio, E., Quarteroni, A. (2002): Mathematical and numerical models for coupling surface and groundwater flows. Appl. Num. Math. 43, 57–74
Fortin, M. (1993): Finite element solution of the Navier-Stokes equations. In: Iserles, A. (ed.) Acta numerica. 1993 Sér, Rouge. Cambridge University Press, Cambridge, pp. 239–284
Girault, V., Raviart, P.-A. (1979): Finite clement approximation of the Navier-Stokes equations. (Lecture Notes in Mathematics, vol. 749) Springer, Berlin
Jäger, W., Mikelić, A. (1996): On the boundary conditions at the contact interface between a porous medium and a free fluid. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23, 403–465
Jäger, W., Mikelić, A. (2000): On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math. 60, 1111–1127
Lions, J.-L., Magenes, E. (1968): Problèmes aux limites non homogènes et applications. Vol. 1. Dunod, Paris
Marini, L.D., Quarteroni, A. (1989): A relaxation procedure for domain decomposition methods using finite elements. Numer. Math. 55, 575–598
Payne, L.E., Straughan, B. (1998): Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modelling questions. J. Math. Pures Appl. (9) 77, 317–354
Quarteroni, A., Valli, A. (1994): Numerical approximation of partial differential equations. Springer, Berlin
Quarteroni, A., Valli, A. (1999): Domain decomposition methods for partial differential equations. Oxford University Press, Oxford
Wood, W.L. (1993): Introduction to numerical methods for water resources. Oxford University Press, Oxford
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© 2003 Springer-Verlag Italia
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Discacciati, M., Quarteroni, A. (2003). Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_1
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DOI: https://doi.org/10.1007/978-88-470-2089-4_1
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2167-9
Online ISBN: 978-88-470-2089-4
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