Journal of Scientific Computing

, Volume 59, Issue 3, pp 775–794 | Cite as

Approximation of the Stokes–Darcy System by Optimization

  • V. J. Ervin
  • E. W. Jenkins
  • Hyesuk Lee


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.


Stokes–Darcy Least squares Finite element method 

Mathematics Subject Classification

65N55 65N30 76D07 76M10 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA

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