On a shape control problem for the stationary Navier-Stokes equations

DOI10.1051/m2an:2000125zbMath0981.76027OpenAlexW1967224776MaRDI QIDQ2707094

Hongchul Kim, Sandro Manservisi, Max D. Gunzburger

Publication date: 4 July 2001

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/197560

zbMATH Keywords

two-dimensional channelLagrangian multiplier methodoptimality systemadjoint methodstationary Navier-Stokes equationsshape gradientoptimal shape control problemviscous drag minimization

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Variational methods applied to problems in fluid mechanics (76M30) Existence theories for optimal control problems involving partial differential equations (49J20) Flow control and optimization for incompressible viscous fluids (76D55)

Related Items (12)

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Cites Work

• On some control problems in fluid mechanics
• Lower-semicontinuity in domain optimization problems
• On the existence of a solution in a domain identification problem
• Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Méthodes de résolution des problèmes approches
• Towards the computation of minimum drag profiles in viscous laminar flow
• Inertial forms of Navier-Stokes equations on the sphere
• An extension theorem for the space \(H_{\text{div}}\)
• A variational inequality formulation of an inverse elasticity problem
• Analysis and approximation for linear feedback control for tracking the velocity in Navier-Stokes flows
• The finite element method with Lagrangian multipliers
• Finite Element Methods for Navier-Stokes Equations
• On the problems of riblets as a drag reduction device
• Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls
• Control/fictitious domain method for solving optimal shape design problems
• Existence of a solution for complete least squares optimal shape problems
• Existence of an Optimal Solution of a Shape Control Problem for the Stationary Navier--Stokes Equations
• Analysis and Approximation of the Velocity Tracking Problem for Navier--Stokes Flows with Distributed Control
• The Velocity Tracking Problem for Navier--Stokes Flows with Bounded Distributed Controls
• On optimum design in fluid mechanics
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