Semi-discrete a priori error analysis for the optimal control of the unsteady Navier-Stokes equations with variational multiscale stabilization

DOI10.1016/j.amc.2015.11.092zbMath1410.49021OpenAlexW2219099431MaRDI QIDQ670996

Fikriye Yılmaz

Publication date: 20 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.11.092

zbMATH Keywords

optimal controlerror estimatestabilized FEMvariational multiscale methodsunsteady Navier-Stokes

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Discrete approximations in optimal control (49M25) Flow control and optimization for incompressible viscous fluids (76D55)

Related Items

Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization

Uses Software

• FreeFem++

Cites Work

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• Subgrid scale eddy viscosity finite element method on optimal control of system governed by unsteady Oseen equations
• A projection-based stabilized finite element method for steady-state natural convection problem
• On some control problems in fluid mechanics
• Finite element error analysis for a projection-based variational multiscale method with nonlinear eddy viscosity
• Infinite-dimensional dynamical systems in mechanics and physics.
• A connection between subgrid scale eddy viscosity and mixed methods
• Comparison of some finite element methods for solving the diffusion-convection-reaction equation
• Optimal control of the convection-diffusion equation using stabilized finite element methods
• A two-level variational multiscale method for convection-dominated convection-diffusion equations
• Stabilized finite element methods for the generalized Oseen problem
• Sufficient second-order optimality conditions for convex control constraints
• Constrained optimal control of Navier--Stokes flow by semismooth Newton methods
• Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
• Optimal Control in Fluid Mechanics by Finite Elements with Symmetric Stabilization
• Finite Element Methods for Navier-Stokes Equations
• Analysis and Finite Element Approximation of Optimal Control Problems for the Stationary Navier-Stokes Equations with Distributed and Neumann Controls
• Analysis and Approximation of the Velocity Tracking Problem for Navier--Stokes Flows with Distributed Control
• Second Order Methods for Optimal Control of Time-Dependent Fluid Flow
• Optimal Controls of 3-Dimensional Navier--Stokes Equations with State Constraints
• New development in freefem++
• A SQP-Semismooth Newton-type Algorithm applied to Control of the instationary Navier--Stokes System Subject to Control Constraints
• A two-grid stabilization method for solving the steady-state Navier-Stokes equations
• A globalization strategy for the multigrid solution of elliptic optimal control problems