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Approximation of the Stokes–Darcy System by Optimization

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Abstract

A solution algorithm for the linear/nonlinear Stokes–Darcy coupled problem is proposed and investigated. The coupled system is formulated as a constrained optimal control problem, where a flow balance is forced across the interface, inflow, and outflow boundaries by minimizing a suitably defined functional. Optimization is achieved by exploiting a Neumann type boundary condition imposed on each subproblem as a control. A numerical algorithm is presented for a least squares functional whose solution yields a minimizer of the constrained optimization problem. Numerical experiments are provided to validate accuracy and efficiency of the algorithm.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, SC, 29634-0975, USA

    V. J. Ervin, E. W. Jenkins & Hyesuk Lee

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  1. V. J. Ervin
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  2. E. W. Jenkins
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  3. Hyesuk Lee
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Correspondence to Hyesuk Lee.

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Partially supported by the NSF under grant no. DMS-1016182.

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Ervin, V.J., Jenkins, E.W. & Lee, H. Approximation of the Stokes–Darcy System by Optimization. J Sci Comput 59, 775–794 (2014). https://doi.org/10.1007/s10915-013-9779-8

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  • DOI: https://doi.org/10.1007/s10915-013-9779-8

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