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

Sergio González-Andrade (), Sofía López-Ordóñez () and Pedro Merino ()
Additional contact information
Sergio González-Andrade: Escuela Politécnica Nacional
Sofía López-Ordóñez: Escuela Politécnica Nacional
Pedro Merino: Escuela Politécnica Nacional

Computational Optimization and Applications, 2021, vol. 80, issue 3, No 11, 979-1025

Abstract: 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.

Keywords: Exact penalization; Bi-viscuous fluids; Nonsmooth optimization; Second order methods; 65K10; 76A05; 49J52; 76M10 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-021-00314-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:80:y:2021:i:3:d:10.1007_s10589-021-00314-2

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-021-00314-2

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().