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Nonsmooth exact penalization second-order methods for incompressible bi-viscous fluids

Author

Listed:
  • Sergio González-Andrade

    (Escuela Politécnica Nacional)

  • Sofía López-Ordóñez

    (Escuela Politécnica Nacional)

  • Pedro Merino

    (Escuela Politécnica Nacional)

Abstract

We consider the exact penalization of the incompressibility condition $$\text {div}(\mathbf {u})=0$$ div ( u ) = 0 for the velocity field of a bi-viscous fluid in terms of the $$L^1$$ L 1 –norm. This penalization procedure results in a nonsmooth optimization problem for which we propose an algorithm using generalized second-order information. Our method solves the resulting nonsmooth problem by considering the steepest descent direction and extra generalized second-order information associated to the nonsmooth term. This method has the advantage that the divergence-free property is enforced by the descent direction proposed by the method without the need of build-in divergence-free approximation schemes. The inexact penalization approach, given by the $$L^2$$ L 2 -norm, is also considered in our discussion and comparison.

Suggested Citation

  • Sergio González-Andrade & Sofía López-Ordóñez & Pedro Merino, 2021. "Nonsmooth exact penalization second-order methods for incompressible bi-viscous fluids," Computational Optimization and Applications, Springer, vol. 80(3), pages 979-1025, December.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:3:d:10.1007_s10589-021-00314-2
    DOI: 10.1007/s10589-021-00314-2
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    References listed on IDEAS

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    1. Georg Stadler, 2009. "Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices," Computational Optimization and Applications, Springer, vol. 44(2), pages 159-181, November.
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