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A Decoupled Preconditioning Technique for a Mixed Stokes–Darcy Model

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Abstract

We propose an efficient iterative method to solve the mixed Stokes–Darcy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of equations. We apply a decoupled preconditioning technique requiring only good solvers for the local mixed-Darcy and Stokes subproblems. We prove that the method is asymptotically optimal and confirm, with numerical experiments, that the performance of the preconditioners does not deteriorate on arbitrarily fine meshes.

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Acknowledgments

The first two authors are partially supported by Ministry of Education of Spain through the Project MTM2010-18427 and the third author is partially supported by the NSF (Grant DMS 1216356).

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Correspondence to Salim Meddahi.

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Márquez, A., Meddahi, S. & Sayas, FJ. A Decoupled Preconditioning Technique for a Mixed Stokes–Darcy Model. J Sci Comput 57, 174–192 (2013). https://doi.org/10.1007/s10915-013-9700-5

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  • DOI: https://doi.org/10.1007/s10915-013-9700-5

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