Fréchet Differentiability of Unsteady Incompressible Navier--Stokes Flow with Respect to Domain Variations of Low Regularity by Using a General Analytical Framework
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Publication:4588838
DOI10.1137/16M1089563zbMath1373.76043MaRDI QIDQ4588838
Michael Ulbrich, Florian Lindemann, Stefan Ulbrich, Michael J. Fischer
Publication date: 2 November 2017
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Fréchet differentiabilityshape optimizationunsteady Navier-Stokes equationsPDE-constrained optimizationmethod of mappings
Fréchet and Gateaux differentiability in optimization (49J50) Existence theories for optimal control problems involving partial differential equations (49J20) Flow control and optimization for incompressible viscous fluids (76D55)
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Cites Work
- Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition
- Application de la méthode des éléments finis à l'approximation d'un problème de domaine optimal. Méthodes de résolution des problèmes approches
- Dynamical shape gradient for the Navier-Stokes system.
- Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces
- Differentiability of implicit functions
- Distributed shape derivativeviaaveraged adjoint method and applications
- Advanced Numerical Methods for PDE Constrained Optimization with Application to Optimal Design in Navier Stokes Flow
- Optimal shape design for the time‐dependent Navier–Stokes flow
- Optimal Vortex Reduction for Instationary Flows Based on Translation Invariant Cost Functionals
- Variational approach to shape derivatives
- On NEMYTSKIJ Operators inLp-Spaces of Abstract Functions
- Newton's Mesh Independence Principle for a Class Of Optimal Shape Design Problems
- The Differentiability of the Drag with Respect to the Variations of a Lipschitz Domain in a Navier--Stokes Flow
- Interpolation for Function Spaces Related to Mixed Boundary Value Problems
- Dynamical systems-based optimal control of incompressible fluids
- On optimum design in fluid mechanics
- Newton's Method for a Class of Optimal Shape Design Problems
- Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
- Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids
- Minimax Lagrangian Approach to the Differentiability of Nonlinear PDE Constrained Shape Functions Without Saddle Point Assumption
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